.... . __ SE9800195 SKI Report 98:18
Analyses of PWR Boron Dilution Consequences with the Arrotta Code
E Johanson H W Cheng B R Sehgal
March 1998
ISSN 1104-1374 ISRNSKI-R--98/18-SE
2 9-24 STATENS KARNKRAFTINSPEKTION Swedish Nuclear Power Inspectorate SKI Report 98:18
Analyses of PWR Boron Dilution Consequences with the Arrotta Code
E Johanson H W Cheng B R Sehgal
Royal Institute of Technology, Division of Nuclear Power Safety, Brinellvagen 60, 100 44 Stockholm, Sweden
March 1998
SKI Project Number 96180
This report concerns a study which has been conducted for the Swedish Nuclear Power Inspectorate (SKI). The conclusions and viewpoints presented in the report are those of the authors and do not necessarily coincide with those of the SKI. Norstedts Tryckeri AB Stockholm 1998 Acknowledgements
The authors wish to thank the Swedish Nuclear Power Inspectorate (SKI) for its support of this project and encouragement. The authors also appreciate the help of the Vattenfall Utveckling AB for providing the neutronic results of SIMULATE-3 for the beginning of Cycle 20 of Ringhals Unit 2. Special thanks must be given to Dr. A.F. Dias and Dr. L.D. Eisenhart from S. Levy Incorporated for their dedicated and continuous assistance in implementation of the boron dilution model into the ARROTTA code. Lastly, the authors are indebted to the staff of Nuclear Power Safety Division of Royal Institute of Technology for the help in preparing this report. Contents
1 Introduction 13
1.1 Knowledge of boron dilution 13
1.2 Backgroud and objectives 15
2 Consideration of boron dilution scenarios 16
3 Dynamic analyses of consequences 18
3.1 General methodology 18
3.2 Preparation for the ARROTTA model 19
3.3 Development of an axial transport model for a diluted slug 22
3.3.1 Model A: a step change in boron concentration 23
3.3.2 Model B: a ramp change in boron concentration 23
3.3.3 Model C: several changes in boron concentration 24
3.4 Dynamic analysis of core response to boron dilution 25
3.4.1 Analyses of Case 1 25
3.4.2 Analyses of Cases 2-4 28
3.4.3 Analyses of Cases 5-6 29
2 CONTENTS 3
3.4.4 Analyses of Case 7 29
4 Sensitivity Studies 35
5 Conclusions and recommendations 37
5.1 Conclusions 37
5.2 Recommendations 38
A Results for Case 1 42
B Results for Case 2 52
C Results for Case 3 62
D Results for Case 4 72
E Results for Case 5 82
F Results for Case 6 91
G Results for Case 7 100
H The EXPICKER file 109
I The AXMOD file 113 List of Figures
3.1 The flow chart for preparation of the ARROTTA input data 19
3.2 The quarter core configuration of Ringhals unit 2, cycle 20 20
3.3 The assembly average exposure (GWD/T) for Ringhals 2, cycle 20 .... 21
3.4 Description of a diluted slug passing the core 31
3.5 Description of an irregular diluted slug 32
3.6 Comparison of total core power for 252 PPM boron dilution 32
3.7 Comparison of core reactivity for 252 PPM boron dilution 33
3.8 Comparison of peak fuel temperature for 252 PPM boron dilution .... 33
3.9 Spatially averaged boron concentration for Case 7 34
4.1 The total core power for varying time steps 36
A.I Change in boron concentration as a function of time for Case 1 42
A.2 Core reactivity as a function of time for Case 1 43
A.3 Total core power as a function of time for Case 1 43
A.4 Core peak fuel temperature as a function of time for Case 1 44
A.5 Fuel enthalpy of Plane 2 as a function of time for Case 1 44
A.6 Fuel enthalpy of Plane 13 as a function of time for Case 1 45
4 LIST OF FIGURES 5
A.7 Fuel enthalpy of Plane 25 as a function of time for Case 1 45
A.8 Nodal power of Plane 2 as a function of time for Case 1 46
A.9 Nodal power of Plane 13 as a function of time for Case 1 46
A. 10 Nodal power of Plane 25 as a function of time for Case 1 47
A.ll Fuel temperature of Plane 2 as a function of time for Case 1 47
A. 12 Fuel temperature of Plane 13 as a function of time for Case 1 48
A. 13 Fuel temperature of Plane 25 as a function of time for Case 1 48
A. 14 Clad outside temperature of Plane 2 as a function of time for Case 1 . . 49
A. 15 Clad outside temperature of Plane 13 as a function of time for Case 1 . . 49
A. 16 Clad outside temperature of Plane 25 as a function of time for Case 1 . . 50
A. 17 Axial void fraction distribution as a function of time for Case 1 50
A. 18 Axial power distribution as a function of time for Case 1 51
B.I Change in boron concentration as a function of time for Case 2 52
B.2 Total core power as a function of time for Case 2 53
B.3 Core reactivity as a function of time for Case 2 53
B.4 Core peak fuel temperature as a function of time for Case 2 54
B.5 Nodal power of Plane 2 as a function of time for Case 2 54
B.6 Nodal power of Plane 13 as a function of time for Case 2 55
B.7 Nodal power of Plane 25 as a function of time for Case 2 55
B.8 Fuel enthalpy of Plane 2 as a function of time for Case 2 56
B.9 Fuel enthalpy of Plane 13 as a function of time for Case 2 56 LIST OF FIGURES 6
B. 10 Fuel enthalpy of Plane 25 as a function of time for Case 2 57
B.ll Fuel temperature of Plane 2 as a function of time for Case 2 57
B.12 Fuel temperature of Plane 13 as a function of time for Case 2 58
B.I3 Fuel temperature of Plane 25 as a function of time for Case 2 58
B.14 Clad outside temperature of Plane 2 as a function of time for Case 2 . . 59
B.15 Clad outside temperature of Plane 13 as a function of time for Case 2 . . 59
B.16 Clad outside temperature of Plane 25 as a function of time for Case 2 . . 60
B.I7 Axial void fraction distribution as a function of time for Case 2 60
B.18 Axial power distribution as a function of time for Case 2 61
C.I Change in boron concentration as a function of time for Case 3 62
C.2 Total core power as a function of time for Case 3 63
C.3 Core reactivity as a function of time for Case 3 63
C.4 Core peak fuel temperature as a function of time for Case 3 64
C.5 Nodal power of Plane 2 as a function of time for Case 3 64
C.6 Nodal power of Plane 13 as a function of time for Case 3 65
C.7 Nodal power of Plane 25 as a function of time for Case 3 65
C.8 Fuel enthalpy of Plane 2 as a function of time for Case 3 66
C.9 Fuel enthalpy of Plane 13 as a function of time for Case 3 66
C. 10 Fuel enthalpy of Plane 25 as a function of time for Case 3 67
C.I 1 Fuel temperature of Plane 2 as a function of time for Case 3 67
C.I2 Fuel temperature of Plane 13 as a function of time for Case 3 68 LIST OF FIGURES 7
C.13 Fuel temperature of Plane 25 as a function of time for Case 3 68
C.14 Clad outside temperature of Plane 2 as a function of time for Case 3 . . 69
C.15 Clad outside temperature of Plane 13 as a function of time for Case 3 . . 69
C.16 Clad outside temperature of Plane 25 as a function of time for Case 3 . . 70
C.17 Axial void fraction distribution as a function of time for Case 3 70
C. 18 Axial power distribution as a function of time for Case 3 71
D.I Change in boron concentration as a function of time for Case 4 72
D.2 Total core power as a function of time for Case 4 73
D.3 Core reactivity as a function of time for Case 4 73
D.4 Core peak fuel temperature as a function of time for Case 4 74
D.5 Nodal power of Plane 2 as a function of time for Case 4 74
D.6 Nodal power of Plane 13 as a function of time for Case 4 75
D.7 Nodal power of Plane 25 as a function of time for Case 4 75
D.8 Fuel enthalpy of Plane 2 as a function of time for Case 4 76
D.9 Fuel enthalpy of Plane 13 as a function of time for Case 4 76
D. 10 Fuel enthalpy of Plane 25 as a function of time for Case 4 77
D.ll Fuel temperature of Plane 2 as a function of time for Case 4 77
D.12 Fuel temperature of Plane 13 as a function of time for Case 4 78
D.13 Fuel temperature of Plane 25 as a function of time for Case 4 78
D.14 Clad outside temperature of Plane 2 as a function of time for Case 4 . . 79
D.15 Clad outside temperature of Plane 13 as a function of time for Case 4 . . 79 LIST OF FIGURES 8
D.16 Clad outside temperature of Plane 25 as a function of time for Case 4 . . 80
D.17 Axial void fraction distribution as a function of time for Case 4 80
D.18 Axial power distribution as a function of time for Case 4 81
E.I Change in boron concentration as a function of time for Case 5 82
E.2 Change in boron concentration as a function of time for Case 5 83
E.3 Nodal power of Plane 2 as a function of time for Case 5 83
E.4 Nodal power of Plane 13 as a function of time for Case 5 84
E.5 Nodal power of Plane 25 as a function of time for Case 5 84
E.6 Fuel enthalpy of Plane 2 as a function of time for Case 5 85
E.7 Fuel enthalpy of Plane 13 as a function of time for Case 5 85
E.8 Fuel enthalpy of Plane 25 as a function of time for Case 5 86
E.9 Fuel temperature of Plane 2 as a function of time for Case 5 86
E.10 Fuel temperature of Plane 13 as a function of time for Case 5 87
E. 11 Fuel temperature of Plane 25 as a function of time for Case 5 87
E.12 Clad outside temperature of Plane 2 as a function of time for Case 5 . . 88
E.13 Clad outside temperature of Plane 13 as a function of time for Case 5 . . 88
E.14 Clad outside temperature of Plane 25 as a function of time for Case 5 . . 89
E.15 Axial void fraction distribution as a function of time for Case 5 89
E.I6 Axial power distribution as a function of time for Case 5 90
F.I Change in boron concentration as a function of time for Case 6 91
F.2 Change in boron concentration as a function of time for Case 6 92 LIST OF FIGURES 9
F.3 Nodal power of Plane 2 as a function of time for Case 6 92
F.4 Nodal power of Plane 13 as a function of time for Case 6 93
F.5 Nodal power of Plane 25 as a function of time for Case 6 93
F.6 Fuel enthalpy of Plane 2 as a function of time for Case 6 94
F.7 Fuel enthalpy of Plane 13 as a function of time for Case 6 94
F.8 Fuel enthalpy of Plane 25 as a function of time for Case 6 95
F.9 Fuel temperature of Plane 2 as a function of time for Case 6 95
F.10 Fuel temperature of Plane 13 as a function of time for Case 6 96
F. 11 Fuel temperature of Plane 25 as a function of time for Case 6 96
F.12 Clad outside temperature of Plane 2 as a function of time for Case 6 . . 97
F.13 Clad outside temperature of Plane 13 as a function of time for Case 6 . . 97
F.14 Clad outside temperature of Plane 25 as a function of time for Case 6 . . 98
F.15 Axial void fraction distribution as a function of time for Case 6 98
F.16 Axial power distribution as a function of time for Case 6 99
G.I Total core power as a function of time for Case 7 100
G.2 Core reactivity as a function of time for Case 7 101
G.3 Core peak fuel temperature as a function of time for Case 7 101
G.4 Nodal power of Plane 2 as a function of time for Case 7 102
G.5 Nodal power of Plane 13 as a function of time for Case 7 102
G.6 Nodal power of Plane 25 as a function of time for Case 7 103
G.7 Fuel enthalpy of Plane 2 as a function of time for Case 7 103 LIST OF FIGURES 10
G.8 Fuel enthalpy of Plane 13 as a function of time for Case 7 104
G.9 Fuel enthalpy of Plane 25 as a function of time for Case 7 104
G.10 Fuel temperature of Plane 2 as a function of time for Case 7 105
G.ll Fuel temperature of Plane 13 as a function of time for Case 7 105
G.12 Fuel temperature of Plane 25 as a function of time for Case 7 106
G.13 Clad outside temperature of Plane 2 as a function of time for Case 7 . . 106
G.14 Clad outside temperature of Plane 13 as a function of time for Case 7 . . 107
G.15 Clad outside temperature of Plane 25 as a function of time for Case 7 . . 107
G.16 Axial void fraction distribution as a function of time for Case 7 108
G.I7 Axial power distribution as a function of time for Case 7 108 List of Tables
3.1 Initial core conditions for Ringhals 2 25
3.2 Diluted slug conditions 26
3.3 Results of comparison for Case 1-4 28
3.4 Comparison results of Position (4,1) for Case 1-4 28
11 Abstract
During the past few years, major attention has been paid to analyzing the issue of reactivity initiated accidents (RIAs), of which the boron dilution event is of very special interest to the countries having pressurized water reactors (PWRs) in their nuclear power delivery systems. The scenario considered is that if an inadvertant accumulation of boron free water in one loop during reactor startup operations of a PWR and the inadvertent startup of the reactor coolant pump (RCP) in the loop. This could then lead to a rapid boron dilution in the core, which can in turn give rise to a power excursion. This report is devoted to studying the potential physical and thermal hydraulic consequences of a slug of diluted coolant entering the core after one RCP start under a couple of postulated cases. The severity of the consequences of such a scenario is primarily determined by the amount of positive reactivity insertion, and they are also related to the reactivity insertion rate. Therefore, in the report, detailed calculations and analyses have been carried out from case to case by using the well-known space-time kinetics code, ARROTTA. As a result, the spatial distribution for nodal power, fuel enthalpy, fuel temperature and clad outside temperature as well as the change in core reactivity, total core power and peak fuel temperature can be provided. In general, the maximum fuel enthalpy, peak fuel temperature, and clad outside temperature, for all the cases considered in the report, do not exceed their respective routine safety limitations because of the strong Doppler effect and moderator temperature feedback, except if the safety limitaions on fuel enthalpy addition for high burnup fuel are drastically reduced.
Keywords: Boron dilution, Pressurized water reactors, Reactivity initiated accidents, ARROTTA, Space-time kinetics, Reactivity feedback, Power excursion, Prompt criticaiity.
12 Chapter 1
Introduction
1.1 Knowledge of boron dilution
In current designs of pressurized water reactors (PWRs), a soluble neutron absorber (also termed chemical shim) such as boric acid which is dissolved in the primary reactor coolant is the most commonly employed method of long-term reactivity control. The chemical shim permits a reduction in the amount of reactivity controlled by control rods, thus resulting in simplified design and reduced costs as well as in improvement in the spatial power distribution. However, it has, at the same time, been well recognized that reactivity-initiated accidents (RIAs) could show up due to inadvertent removal of boric acid from the PWR core or to dilution of the reactor coolant system (RCS)[1, 2].
Formally, the boron dilution transients fall into two main categories[3]. One is the classic category which is assumed to affect the entire RCS in a homogeneous manner and consequently is global dilution. In the routine safety analysis, most of studies performed as early as in sixties or seventies were mainly limited to this category, with assumptions which gives rise to slow decrease in boron concentration since even the largest dilution flow, theoretically available, is still small compared with the volume of the RCS. The reactivity insertion rate is, therefore, slow corresponding to the slow change in boron concentration. Obviously, that may permit sufficient time for the identification of the problem and operator action.
The other category is defined as local (or heterogeneous) boron dilution events where the diluted coolant is assumed to be heterogeneously distributed in the reactor core[3, 4]. It was reported that the reactor could be brought to prompt criticality with resulting fuel damage when a slug of diluted or boron-free water is rapidly forced into the core by reestablishment of natural circulation or restart of reactor coolant pumps (RCSs)[3, 4, 5].
13 CHAPTER 1. INTRODUCTION 14
In some cases, the core damage frequency for the local boron dilution, that occurs in the Westinghouse designed PWRs, was estimated by a probability safety assessment (PSA) to be from 9.7E-6/year to 2.8E-5/year, which is relatively high when compared to the desirable objectives[6]. Therefore, during the past few years, much attention has been paid to investigating the local boron dilution transients in order to clarify if any challenge could be posed to the core integrity by this issue.
The mechanisms of creation of local dilution are quite complicated. Two mechanisms to lead to a local boron dilution have been identified in the literature, i.e., external and inherent boron dilution mechanisms [7]. By external dilution we mean occasions where diluted or boron-free water slug is generated by injection from an external source such as failure in the reactor charging system, leaking thermal barrier in RCPs housing, accu- mulator filled with pure coolant during refueling, a leak from secondary to primary (re- versed) side of the steam generator (SG) or RCP sealing injections. An inherent dilution mechanism may occur in a number of accident scenarios, when dilution could take place through inherent phenomena during such accidents as in small break loss of coolant acci- dents (SBLOCA)[5, 8], steam generator tube ruptures (SGTR) and anticipated transient without scram (ATWS). During these postulated scenarios, reflux/boiling-condensing heat transfer mode prevails to remove the decay heat inside the primary system during natural circulation [7, 9]. Consequently, the boron-free or slightly diluted condensate could accumulate as a slug in a stagnant loop seal of the primary system due to the chemical property of insolubility of boric acid into steam. The subsequent change in flow conditions, such as loop seal clearing, restart of the RCPs, and restart of natural circulation, may supply an effective way to sweep the slug of diluted water into the core. However, the buoyancy and turbulent thermal mixing process along the path form the stagnant loop seal to the core may increase the boron concentration of the diluted stream sufficiently to prevent a power excursion leading to fuel failure[lO, 11].
As discussed above, a rigorous and all-round evaluation of a boron dilution accident should include:
• development of boron dilution scenarios involving unborated or diluted slug forma- tion mechanisms, estimation of boron concentration and temperature distribution, and slug size, • transport of a unborated slug from a stagnant zone through the core with restart of RCPs or natural circulation under single phase, subcooled, two-phase or possibly stratified conditions, which involves a most important transport phenomenon, i.e., thermal mixing between unborated and borated coolant, and • dynamic response of reactor core to the diluted or/and colder coolant slug when passing through the core as a homogeneous or strongly heterogeneous mixture.
Slug formation mechanisms entail a thorough plant-dependent investigation that cov- CHAPTER 1. INTRODUCTION 15 ers all the possible boron dilution events. Slug transportation evaluations can be per- formed either by experimental modeling or by using 3D computational fluid dynamics codes such as TRAC[12], PHOENICS[13] or C0MMIX[14]. More exact analysis of dy- namic response of reactor core essentially requires 3D reactor dynamics models such as SIMULATE-3K or ARR0TTA[15] owing to the spatial non-uniform distribution of boron concentration in the core inlet and of necessity to calculate the ramp effects.
1.2 Backgroud and objectives
So far, there has already been a lot of work done on boron dilution mainly by Sweden, USA, France, Finland. However, most of attention of the researchers in this field has been placed on how the diluted coolant is mixed with undiluted coolant when it is transported from its generating location through the downcomer, finally to the lower plenum of the core[16]. As for the dynamic core response due to boron dilution inside the core, it was analyzed simply either by the point kinetics model or by a static core analyzing code, for example, the static SIMULATE-3 employed in the S. Jacobson's dissertation, thus absolutely neglecting various transient feedback effects or/and mitigating the extent of heterogeneity of boron concentration distribution. So, in respect of this fact, this report will concentrate on investigation of the dynamic consequences of the boron dilution rather than that of mixing by taking advantage of the well-known three-dimensional space- time kinetics code, i.e., ARROTTA developed by EPRI. In addition, the time-dependent spatial distribution of boron concentration in the core inlet required by ARROTTA is obtained either simply by assumption or directly from experimental results of model tests on boron dilution transient which were performed before by B. Hemstrom and N.G. Andersson at the Alvkarleby Laboratory of Vattenfall Utveckling AB[16].
Therefore, this report will aim at analyzing in detail how the dynamic consequences of boron dilution vary with the amount and different spatial distributions of a diluted slug, and the changing fashion of boron concentration such as a step-like way or a ramp way. Meanwhile, it will be explored how the temperature feedback acts on the core and nodal power, reactivity, fuel and clad temperature, fuel enthalpy and so on in the process of boron dilution. Thus, it will be clarified if and under what conditions the boron dilution accident could result in fuel damage. A more recent issue of fuel performance is the finding that highly burned LWR fuel could suffer damage with fuel enthalpy additions much less than those assumed for the fresh fuel. Thus the boron dilution RIA event may provide increase in enthalpy for a high burnup fuel, which may exceed the limits found experimentally. Chapter 2
Consideration of boron dilution scenarios
Ringhals unit 2 is chosen as the reference plant for studying boron dilution events in the report. This is a 3-loop and two-turbine Westinghouse-designed PWR and con- structed in 1970. The reactor was taken into operation in 1970 and commercial operation set out in 1975. In this report, a category of boron dilution scenarios, which is charac- terized by rapid boron dilution transients with start of one reactor coolant pump, is postulated to take place at the beginning of cycle 20 of Ringhals unit 2 (see Figs. 3.2 and 3.3).
A rapid boron dilution transient may be initiated under the following occasions:
At first, the reactor is assumed be at a critical hot-zero-power (HZP) state during boron dilution with all the control rods withdrawn out of the core, and with all the RCPs idle. Meanwhile, it is presumed that the unborated water enters the reactor coolant system from the refuelling water storage tank (RWST) or the chemical volume control system (CVCS) due to manual errors or mechanical malfunctions, and as a result accu- mulates in one of the three stagnant loop seal. When the RCP in the diluted loop is started, a slug of unborated water will be forced down the downcomer and subsequently through the reactor core. It is also assumed that reactor operators do not have sufficient time to manually shut down the reactor.
In addition, it is also possible that a similar rapid boron dilution event is initiated during a small break loss of coolant accident (SBLOCA). It is assumed that a SBLOCA takes place. The natural circulation will cease as the vessel level falls below the bottom of the hot leg. This leads to condensation of steam produced in the steam generator and possible filling of the steam generator outlet plenum with boron-free water. If a pump
16 CHAPTER 2. CONSIDERATION OF BORON DIL UTION SCENARIOS 17 startup is introduced, the boron-free water accumulated in the secondary side of the SG will be added to the vessel lower plenum. Chapter 3
Dynamic analyses of consequences
3.1 General methodology
In order to evaluate the response of the core to the injection of a slug of diluted water, a three-dimensional dynamic core code is required. That code should be comprised of a three-dimensional neutron kinetics model which is coupled at least with a one- dimensional thermal hydraulics in multiple channels model if a three-dimensional thermal- hydraulics model is unavailable. It is also required to have a capability of tracking the boron transport throughout the core for a given distribution at the core inlet. From all the associated codes at hand, the ARROTTA code is thus selected and regarded as a qualified candidate although it lacked a model of the boron transport which will be discussed later.
The ARROTTA code developed by EPRI is a three-dimensional space-time kinet- ics code coupled to one-dimensional multiple-channel thermal hydraulics. Hot channel analysis including local fuel and cladding temperatures, and fuel enthalpies is partially provided. It can be applied for solving the static and transient problems in a three- dimensional Cartesian coordinate system, such as steady-state eigenvalue problems with or without critical boron search, rod ejection accidents, xenon and samarium transients and so on.
The ARROTTA code utilizes the analytical nodal method (ANM) for the spatial treatment in the three-dimensional neutron diffusion equations while a standard finite difference technique, i.e., the theta method, is applied for the treatment of the time variable in the transient neutron diffusion equation or the precursor equation.
The thermal-hydraulic model is comprised of a fluid dynamics model and a heat
18 CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 19 transfer model. The fluid dynamics is confined to an inhomogeneous, nonequilibrium two- phase flow. The heat conduction model is based on spatially averaged, time-dependent equations for the averaged pellet temperature. Besides, it has been subject to an extensive verification and validation effort for a variety of transients, including comparisons with actual plant operational data as well as other codes. Hence, ARROTTA is supposed to be one of the codes best suited for the analysis of the reactivity effects of the reactor core, e.g. the boron dilution transients.
3.2 Preparation for the ARROTTA model
Before the dynamic analyses on the boron dilution transients for Ringhals unit 2, cycle 20, are performed with the ARROTTA code, the cross sections and discontinuity factors of assemblies, the composition-related data, the kinetics parameters and others should be prepared for the
CASMO-4
\ 1 \ 1
SIMULATE-3 ]NORGE-P
\ ( \ /
EXPICKJER NTPREP
\ f \ f REBLEND
\ f ARROTTA
Figure 3.1: The flow chart for preparation of the ARROTTA input data
ARROTTA input. Therefore, a standard computational sequence was developed to CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 20 produce the major portion of the ARROTTA input as shown in Fig. 3.1. At the be- ginning, the CASMO-4 program[18], which is a multi-group two-dimensional integral transport theory code and extensively validated, is utilized for obtaining all fuel lattice and reflector data. These lattice physical data are, in general, a compound function of fuel enrichment, burnup, boron concentration, moderator temperature, fuel temperature, void in coolant and control rod number, burnable poison number, and so on. 1 2 3 4 5 6 7 8 9
1 9 10 11 13 14 9 12 14 27 9 3.4 W/O
2 10 11 12 10 10 11 12 11 27 10 3.5 W/O
3 11 12 9 13 10 13 9 28 27 11 3.5 W/O 8 Gd 6.0 W/O
4 13 9 13 9 10 14 11 28 12 3.5 W/O 8 Gd 5.0 W/O
5 14 12 9 10 13 9 28 27 13 3.5 W/O 12 Gd 6.0 W/C
6 9 11 13 14 11 28 28 14 3.5 W/O 12 Gd 5.0 W/C
REFLECTOR WITH 7 12 12 9 9 28 28 27 BAFFLE
REFLECTOR WITH 8 14 11 28 28 27 28 BARREL
9 27 27 27
Figure 3.2: The quarter core configuration of Ringhals unit 2, cycle 20
Fig. 3.2 gives the quarter core layout for Ringhals unit 2, cycle 20, as well as the description of fuel and reflector types, where there are five fuel types and two reflector types. So, the data were generated with CASMO-4 for fuels containing either 0, 8, 12 burnable poison (BP) rods, and also for four reflector types if including top and bottom reflectors. Note that each BP contains either 5.0% or 6.0% w/o Gd. In addition, each run with CASMO for every assembly has to comprise all necessary minimum branch cases with different moderator and fuel temperatures, different boron concentrations, and with or without contral rods, so that all kinds of feedback relations can be subsequently established by the following processing codes in the ARROTTA input deck.
NORGE-P sorts and formats the lattice data produced by CASMO-4 into a simpler form which contains only the data needed by the ARROTTA model. For each particular fuel type or reflector type, one data file is generated. NTPREP reformats all the data files provided by NORGE-P into a binary library. This library contains the lattice physics CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 21 data of all the fuel and reflector types used in the analyzed boron dilution transient.
Since ARROTTA lacks a fuel depletion model, a three-dimensional steady-state de- pletion code such as SIMULATE-3 is taken advantage of to determine the fuel assembly exposure and moderator density history at the beginning of cycle 20 of Ringhals unit 2. The resulting reloading pattern and exposure distribution for the beginning of cycle 20 of Ringhals unit 2 is shown in Figs. 3.2 and 3.3, where the less shaded assemblies stand for fresh fuel while the more shaded represent more highly depleted fuel assemblies.
A connection between SIMULATE-3 and ARROTTA is accomplished via a special processing code EXPICKER (see Appendix H for details) developed by ourselves. EX- PICKER can transform the data dumped from the SIMULATE-3 into a binary library which REBLEND can read. Consequently, all the data generated by REBLEND eventu- ally flow to the ARROTTA input decks.
26.986 13.071 20.546 0.000 18.886 0 000 0 000 ;• .1, *•
13.081 32.887 13.602 31.253 13.IVi IS 01S 0 000 11 Wo
20.584 13.674 28 695 0.000. 31 24*5 0 000
0000 32.176 0000 29 80"* 11 <>l>4 0 000 ^2 2^4
18.858 12.372 W 09S 11611 0 000 -40.916
44452 ] 5 0f)7 oooo 0 000 3J «)«?
0 000 0 OnO 2s.5i5
0000 11660
Figure 3.3: The assembly average exposure (GWD/T) for Ringhals 2, cycle 20 CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 22
3.3 Development of an axial transport model for a diluted slug
When the ARROTTA code is employed to analyze the boron dilution transient, a significant problem occurred that ARROTTA can not handle an axial variation of boron concentration. The original ARROTTA model essentially demands that the boron concentration be constant in the axial direction during each time step while this restriction can be relaxed in the radial plane. So, the ARROTTA code has to be modified to incorporate a boron transport model for overcoming this inadequacy.
Since the report is not readily going to study any mixing phenomenon with the diluted slug passing from the loop seal to the lower plenum, and our major concern is just that how and why the active core reacts to the incore boron dilution, some assumptions are used:
• The spatial distribution of boron concentration in the core inlet as a function of time is given in advance. • Any mixing of diluted coolant is not accounted for during the propagation of the slug in the core. • The slug is assumed to enter the core radially uniformly across the entire channel or a node while the boron concentration for different channels may be allowed to differ from each other. • The constant speed used for the slug front is assumed to be V cm/s which should be in agreement with the corresponding flow rate of the channel. • It is assumed that the slug advances in the core as a whole. In other words, there is no change inside the slug during its movement and the speed of every position in the slug is identical to that of the slug front.
In addition, the core is uniformly partitioned into N+l intervals in the axial coordinate (see Fig. 3.4), where No. 0 and No. N+l intervals stand for bottom reflector and top reflector, respectively. Once the diluted slug front reaches the core inlet, the original boron concentration of the core inlet will change to the one of the diluted slug. This changing fashion may be taken either as a step or as a ramp in the report. Further, in order to determine at what time the changed boron concentration arrives at the bottom reflector, an imaginary starting position for the slug front and certain break points in the slug are given in centimeters below the core entrance. Different break points represent different boron concentration levels. This technique can translate the time-dependent CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 23 boron concentration of channels into a space-dependent function as the position of the slug front, which is more easily realized in the ARROTTA code.
For more details in clearly expounding the model, the following three situations are considered in this report.
3.3.1 Model A: a step change in boron concentration
In this case, only two break points, i.e., the slug front and tail, are given. The boron concentration for the entire slug is all the same. Besides, the boron concentration of some position at which the slug front is arriving is being changed immediately to that of the slug front. That means a step change in boron concentration takes place.
Let Corg and Cnew be the boron concentration of the diluted slug, respectively. Addi- tionally, let us assume that the bottom plane of the bottom reflector is the axial origin, and that the initial axial coordinates of the slug front and tail are, respectively, ZF(t0) and ZT(t0), where t0 stands for the initial time of a boron dilution transient. With those denotations, the boron concentration of node K at tnow, CK, is then determined by:
(COrg • {(k + l)-dz- ZF{inow)) + Cnew • (ZF(tnow) - k • dz))/dz ,k • dz < ZF(tnow) < (k + 1) • dz ((k + 1) • dz - ZT(tnow)) + Corg • {ZT(tnow) - k • dz))/dz ,k-dz
3.3.2 Model B: a ramp change in boron concentration
For this case, the slug front is not like a sharp wave front, but its boron concentration takes time to change from the beginning of the transient. Apart from this point, other conditions are similar to the assumptions in Model A. Such a ramp change is as if the CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 24 mixing is happening there during advancement of the slug front. If it is assumed that the boron concentration of the slug front is linearly changed from Corg to Cnew between to and tend, then the boron concentration change per centimetre is:
- Corg)/(V • tend ~ ZF(t0)).
Thus, the boron concentration of node K at tnow can be calculated by:
-1) -dz - ZF(tnow)) + (Corg - Cunit • (ZF(tnow) - k • dz) • (ZF(tnow) - k • dz)/dz, k-dz< ZF(tnow) < (k + 1) • dz
(Zo(tn0w) fc ' dZ) -\- (Cneuj (^unit ' ((k "T 1) * UZ Zb(tnow)J /2) • ((k + l)-dz- ZS(tnOu,)))/dz, k-dz< ZS(tnow) <(k + l)-dz
k-dz< ZF(tnow) + Cunit(ZF(tnow) -(k + 1/2)) • dz, otherwise where
ZS(tnow) = (tnow ~ tend) ' V
3.3.3 Model C: several changes in boron concentration
In this case, let us assume tha there are M break points in the slug. Meanwhile, the boron concentration and imaginary corresponding spatial position for each break point have to be given as well. In addition, an assumption is introduced that boron concentration between break points is linear as in Model B. For all the flow channels, the positions of those break points should be calculated during every time step. Thus, by knowing between which break points the node is, the boron concentration for the node entrance and exit can be calculated, and then an average for the node can be easily calculated. If one of the break points is located in that particular node, the calculations are somewhat more complicated. An average is then calculated on each side of that point, and with these two values the boron concentration for the node is finally calculated taking into account at what distance from the node entrance the break point is. For details, please take a look at Appendix I. CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 25
3.4 Dynamic analysis of core response to boron di- lution
For all the following boron dilution events to be studied, it is assumed that a large amount of diluted coolant accumulated in a stagnant loop seal due to malfunctions is swept to the core just by start of one reactor pump while other pumps are idle. So, all channel flowrates are around one third of full flowrate, corresponding to which the speed of the diluted slug should be 1.56 m/s in the case of Ringhals 2. Meanwhile, Ringhals 2 is thought to be in a critical hot-zero-power (HZP) state with all control elements withdrawn out of the core, which means that the excess reactivity is zero. Moreover, it is assumed that all the control elements are stuck during boron dilution. Note that the critical boron concentration (approximately 1252 ppm) was searched by using the ARROTTA code rather than SIMULATE-3, and the result is slightly different from that of SIMULATE-3. That is mainly because their cross section models used are different. Table 3.1 gives all initial core conditions required by the ARROTTA code.
Table 3.1: Initial core conditions for Ringhals 2
Initial power 1 MW Initial core temperature 559 K (HZP) Initial critical boron 1252 PPM Position of CRDs Fully withdrawn Flowrate 1/3 full flowrate System pressure 2250 psia
In general, the amount of positive reactivity due to boron dilution inserted into the core is significantly influenced by several factors such as geometric shape of a diluted slug, volume of a diluted slug, mixing degree, and velocity of a diluted slug. Therefore, in this section, the boron dilution reactivity is evaluated by specifying seven particular cases as shown in Table 3.2.
3.4.1 Analyses of Case 1
Boron dilution is, in Case 1, assumed to occur uniformly across the core, and its change in boron concentration is represented as a sharp wave front (step) by 252 ppm, 352 ppm, 452 ppm, and 552 ppm with respect to the critical boron concentration (1252 ppm), respectively. The boron dilution transient begins at 2.564 seconds, and the final time for the transient is 15 seconds. Fig. A.I describes how the boron concentration for the different planes varies with time. CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 26
Table 3.2: Diluted slug conditions
Case Change in boron Slug geometry Changing manner concentration, PPM 1 ~250 Semi-infinite and uniform Step 2 ~350 Semi-infinite and uniform Step 3 ~450 Semi-infinite and uniform Step 4 ~550 Semi-infinite and uniform Step 5 ~250 Semi-infinite and non-uniform Step 6 ~250 Semi-infinite and non-uniform Ramp 7 Given Non-uniform 8 m3 slug Given
The volume of the diluted slug is semi-infinite, which means that the diluted slug is continuously provided from the diluted circuit until the final time is reached. Such a situation might take place when there is enough external boron-free water to fill most of space of the RCSs due to manually or mechanically errors.
The core reactivity and corresponding power production are shown in Figs. A.2 and A.3, respectively. Clearly, the power trace is typical of a prompt-critical reactivity excursion. At 1.0 second from the beginning of the transient when the lower half of the active core has been almost occupied with the diluted slug, a sharp reactivity rise shows up with a maximum of reactivity of 1.56 $ which correspondingly results in a power spike. However, this is terminated by the Doppler feedback due to a large increase in fuel temperature (see Fig. A.4). During this power excursion, a local power oscillation could be observed from Fig. A.3. This is mainly because of interactions of various reactivity feedback effects.
• In the beginning, the reactor period is shorten with a large reactivity successively inserted into the core. As a result, the core power rises drastically until the Doppler effect causes sufficient negative feedback to terminate the power rise. At this time, the Doppler feedback is robust since the core does not have enough time to remove most of the energy scattered in the fuel to the coolant. So, the power sets out to decline, and the first power peaking is thus formed. • Subsequently, the power feedback effect alleviates with the decrease of the power. Until the time at which the total reactivity feedback does not exceed the reactivity owing to the boron dilution, the second power peaking sets out. If there were no delayed neutrons, then this power oscillation would not die out, and eventually disappear. • In reality, as the delayed neutron precursors accumulate in the core, and the mod- CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 27
erator temperature and/or void feedback start to act after a sufficiently long time (around 5 seconds), the power oscillation process certainly decline gradually, and eventually the reactor arrives at a new steady state.
Although the maximum power is up to about 15000 MW, what is the most important in determining the fuel response is the very integral of power, i.e., the total fission energy that is deposited in the fuel. The energy deposition brings about corresponding increase in both fuel temperature and enthalpy. The radial enthalpy is generally an important quantity used to clarify whether or not catastrophic fuel failure has taken place.
The fuel enthalpies for Positions (1,1), (4,1) and (6,1) as shown in Fig. 3.2 in Planes 2, 13, and 25 are indicated in Figs. A.5-A.7, where it is observed that the fuel enthalpies of Planes 2 and 13 are much greater than that of Plane 25. The fuel enthalpy of Position (4,1) is greater than those of other two nodes in Planes 2 and 13 while the enthalpy of Position (1,1) is greatest of these three nodes even though Position (1,1) is a spent fuel assembly whose exposure is 26.983 MWD/KGU, and Position (4,1) is a fresh fuel assembly. However, no fuel assembly is found whose local peak fuel enthalpy is not acceptable compared to the criterion for catastrophic fuel damage. This is taken to be 280 cal/g which is the acceptance criterion for design-basis reactivity-initiated accidents calculated for licensing. In addition, the behaviour of fuel assemblies with high burnup (e.g. Position (6,1)) should be examined with more attention during boron dilution because they could more easily suffer a damage than the fresh fuel assemblies. Hence, the enthalpy criterion may change because of concerns about high burnup fuel behavior. In that case, these results could be reinterpreted with the new criterion.
In this case, two-phase flow is observed in the upper part of channels, so that a large amount of void can be generated which leads to significant negative feedback and would in turn affect the fuel behavior. Fig. A.17 indicates the axial void change as a function of time. Of course, the void feedback effect also have influence on the axial power distribution. Fig. A. 18 indicates how the axial power change during the boron dilution transient, which clearly shows that the axial power is always situated within the lower half of the core since the coolant is still subcooled there while the coolant in the upper core may be overheated, and more voiding occurs.
As for nodal power, fuel and cladding outside temperatures as shown in Figs. A.8- A.16, there exist pretty large margins between the peak fuel temperature and cladding outside temperatures and their respective acceptance criteria, and thus DNB and local cladding oxidation could not be expected. CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 28
3.4.2 Analyses of Cases 2-4
For Cases 2-4, the final boron concentration is assumed to be 900 ppm, 800 ppm, 700 ppm, respectively, while it is just 1000 ppm for Case 1 (see Figs. B.I, B.I, and D.I). Other pre-conditions are identical to those of Case 1. So, it is expected that a larger reactivity will be inserted into the core. Table 3.3 gives the results of comparison of the core power, reactivity, peak fuel temperature while Table 3.4 provides the results of comparison for Position (4,1) since the channel which contains Position (4,1) is probably hottest channel.
Obviously, the severity of the boron dilution transients depends on the degree of boron dilution. In Case 4, the maximum fuel temperature has been up to 1936 °C, and the maximum fuel enthalpy at Position (4,1) is as high as 179 cal/g. However, the maximum clad outside temperatures do not change so much even in Case 4, and they are very close to the saturated temperature. So, the effect of two-phase flow heat transfer does not worsen, and the coolant does not dry out on the surface of the clad, either.
In addition, all the results for these three cases are listed in Appendices B, C and D.
Table 3.3: Results of comparison for Case 1-4
Case 1 2 | 3 4 Maximum power (MW) 15692 32121 52404 67568 Final power (MW) 354 384 395 408 Maximum reactivity ($) 1.56 1.90 2.23 2.49 Maximum fuel temperature (°C) 1047 1355 1693 1936
Table 3.4: Comparison results of Position (4,1) for Case 1-4
Case 1 3 4 Maximum Plane 2 672 888 1114 1343 fuel Plane 13 816 720 649 620 temperature (°C) Plane 25 463 420 401 385 Maximum Plane 2 310 324 341 347 clad outside Plane 13 348 348 348 348 temperature (°C) Plane 25 347 347 346 346 Maximum Plane 2 86 115 147 179 fuel Plane 13 105 93 83 79 enthalpy (cal/g) Plane 25 58 53 50 48 CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 29
3.4.3 Analyses of Cases 5-6
In Cases 5-6, the diluted slug is assumed to enter the core in an irregular shape as shown in Fig. 3.5. The boron concentration for the red region is changed from 1252 to 900 ppm while it is changed just to 1050 ppm for the blue region. As a result, the averaged change in boron concentration is only 252 ppm over the entire radial plane. Such an assumption is more realistic than a homogeneous boron dilution adopted in the previous cases if mixing is taken into account. In reality, mixing absolutely results in an inhomogeneous boron concentration distribution in the lower plenum.
In addition, a ramp change in boron concentration is introduced in Case 6 which seems like a mixing process is happening in the lower plenum during advancement of the slug front (see Figs. E.I, E.2, F.I and F.2), while Case 5 assumes a step change as in Cases 1-4.
The results of comparison of Case 1, 5 and 6 are shown in Figs. 3.6-3.8. Other results are listed in Appendices E and F. Apparently, no big difference in total core power and reactivity could be made between Cases 1 and 5 by an irregular diluted slug. However, such an irregular diluted slug may bring about a large radial local power peak factor as Fig. 3.8 shows, which should be examined with more attention.
As compared to a step change, a ramp change clearly delays the time at which the total core power, reactivity and peak fuel temperature get to climax. Meanwhile, all the curves for power, reactivity, fuel temperature and so on look smoother than a step change. This is due mainly to the fact that the reactivity insertion rate for a ramp change is smaller, and the integrated boron discrepancy over the transient against the critical boron concentration is lower than a step change. Besides, a ramp change can give the reactor system sufficient time for various reactivity feedbacks, especially moderator temperature an>! void effects to take effect. Hence, mixing is a very important protective mechanism for boron dilution.
3.4.4 Analyses of Case 7
In all above discussed sections, both the spatial distribution and the time-dependent change of boron concentration in the core inlet are obtained simply by some assump- tions. Hence, those conclusions drawn from Cases 1-6 tend to be conservative and not realistic. In fact, when the diluted slug or boron-free water is forced into the core plenum from the loop seal, it certainly mixes more or less with the undiluted coolant inside the core. Therefore, in order to more realistically analyze the dynamic response to the boron dilution, it is necessary that a reasonable and acceptable boron distribution be given by using a fluid dynamics code or doing model experiments. The results obtained from CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 30 model experiments seem to be more accurate than those calculated by a fluid dynam- ics code in a sense that fluid dynamics calculations inevitably give rise to a numerical diffusion problem.
In this section, the dynamic analysis is based on the work on physical modeling of a rapid dilution transient which was done by H. Tinoco, B. Hemstrom and N.G. Andersson at the Alvkarleby Laboratory of Vattenfall Utveckling AB [16]. In this work, boron dilution events are characterized by a rapid start of a reactor coolant pump with a slug of unborated water (approximately 8 m3) present in the RCS pipe. Model tests were carried out in a 1:5 model of Ringhals 2. As a result, a space/time-dependent distribution of boron concentration in the core inlet can be obtained through measuring. In the meantime, it was demonstrated that a substantial mixing occurs before the slug reaches the core.
Fig. 3.9 describes how the spatially averaged boron concentration varies during 30 seconds. This figure is made by taking out 15 points from the corresponding figure on Page 18 of the reference [16]. Meanwhile, the spatially averaged boron concentration changes linearly between every two points. As for the space-dependent boron concen- tration distribution for a particular time except at 6.0 and 6.5 seconds, it is assumed to be distributed homogeneously and uniformly all over the radial plane. For 6.0 and 6.5 seconds, two concrete spatial distributions are given according to Figs. 13a and 13b of the reference [16], correspondingly.
Since the boron concentration distributions at 6.0 and 6.5 seconds are asymmetric, the core geometry is taken to be a half core, not a quarter core used in Cases 1-6 when running the ARROTTA code. All the results for this case are shown in Appendix G, where it is again observed that there is a sharp power rise (super prompt criticality) at 6.5 seconds after the slug has moved into the core as in Cases 1-6, but the power begins to decrease significantly at about 10 seconds when the spatially averaged boron concentration starts to increase as shown in Fig. 3.9, in other words, the undiluted water re-enters the core thereby rapidly reducing the power. Owing to this reason, the change in reactivity becomes a little more complicated. The maximum reactivity is up to 1.75 $ while the minimum goes down to -1.0 $. The void effect is as well a main contribution to such a large negative reactivity as shown in Fig. G.16 where at about 10.0 seconds the void faction reaches maximum, and then decreases to a small value. The maximum core peak temperature is 1180 °C which is still a safe one. The fuel enthalpy for all nodes is within about 120 cal/g while the maximum clad outside temperature (approximately 350 °C) is very close to the saturated temperature. Thus, the fuel or cladding failure induced by DNB is not to be expected in this case. CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 31
Upper plenum
k+1 k A diluted slug
Lower plenum
Figure 3.4: Description of a diluted slug passing the core CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 32
1050 PPM
900 PPM
Figure 3.5: Description of an irregular diluted slug
100000 1 ! 1 I — Homogeneous dilution in a step 10000 r — - Inhomogeneous dilution in a step — Inhomogeneous dilution in a ramp 1000 r
100
10
1 0 6 9 12 15 TIME (s)
Figure 3.6: Comparison of total core power for 252 PPM boron dilution CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 33
2.00 1 i— -i . ' 1 I - I | I I — Homogeneous dilution in a step 1.50 - 1 — Inhomogeneous dilution in a step — Inhomogeneous dilution in a ramp 1.00 1 . , l
"v 0.50 \ \ , , - - I 0.00 -0.50 s^- ; -1.00 i , , i , , i 6 9 12 15 TIME (s)
Figure 3.7: Comparison of core reactivity for 252 PPM boron dilution
1200
u 1000
D 800
u5 600
400 — Homogeneous dilution in a step — Inhomogeneous dilution in a step 200 Inhomogeneous dilution in a ramp 0 6 9 12 15 TIME (s)
Figure 3.8: Comparison of peak fuel temperature for 252 PPM boron dilution CHAPTER 3. DYNAMIC ANALYSES OF CONSEQUENCES 34
1300
1200
OH zo p 1100
U 8 1000
900 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 TIME (s)
Figure 3.9: Spatially averaged boron concentration for Case 7 Chapter 4
Sensitivity Studies
In order to determine to what extent all the results done with the ARROTTA code in Chapter 3 could be acceptable, sensitivity studies have to be performed. The accuracy of the modified ARROTTA code with a new axial model of slug transport is mainly depen- dent on how to determine acceptable values for selected parameters for a boron dilution analysis. The parameters evaluated include axial and radial mesh spacing, convergence on a transient fixed-source problem, and time step size.
In chapter 3, these crucial parameters are defined as below:
• The standard mesh of 1 by 1 radial mesh per assembly and 24 axial mesh points in the active core with two points in the axial reflectors has been tested to give a converged result. • It was demonstrated that the default convergence criteria are not sufficiently tight for the boron dilution transient. Recommended values are: CONEIG 1.0E-05 CONDEG 1.0E-03 CONSRT 1.0E-04 CONPOW 1.0E-03
• The time step size needed to obtain an accurate calculation of a power spike is 0.001 second for a super prompt critical boron dilution transient. Larger time step sizes must give a larger peak which is conservative. Before the diluted slug front and/or tail totally leaves the core, larger time step sizes are strictly forbidden to be used because a larger time step size can distort nodal boron concentration as explained in Chapter 3. The variation of total core power with time step size for Case 1 is shown in Fig. 4.1. It is noticed that the curve for a 0.001 second time step almost
35 CHAPTER 4. SENSITIVITY STUDIES 36
fully overlap the one for a 0.0005 second time step. Therefore, a time step of 0.001 second employed in analysis of boron dilution transients does make sense.
100000 r— i
10000 r 'A ^ -- for 0.01 1 1000 — for 0.001 - for 0.0005 w 100 0 10 r
1 0 1 TIME(s)
Figure 4.1: The total core power for varying time steps Chapter 5
Conclusions and recommendations
5.1 Conclusions
Several boron dilution transients have been analyzed with the ARROTTA code. It is demonstrated that although the severity of boron dilution events is affected by the diluted slug geometry, mixing with the undiluted coolant in the reactor vessel, the manner of boron concentration change and others, the cases analyzed in the report have indicated that the maximum fuel enthalpy deposition, peak fuel temperature, and cladding surface temperature do not exceed their respective licensing acceptance criteria for design-basis reactivity-initiated accidents. That is mainly because various strong reactivity feedbacks take effect. However, if the fuel enthalpy deposition acceptance criteria are modified, as they may be for the high burnup fuel, the RIA caused by boron dilution may need more detailed evaluations. In particular, the mixing phenomena will need greater depth of analyses.
In summary, detailed conclusions are given as follows:
• As the diluted coolant flows into the core, a large reactivity is inserted into the core, and consequently the reactor very quickly reach a super prompt criticality, which results in a power spike. However, the power spike is terminated by the strong Doppler effect. The void effect may gain ground at the later stage of the transient, and together with the power reactivity feedback, they further cut down the power escalation.
• For all cases, two-phase flow is observed in the upper core. The void fractions, however, are low, and the CHF is never reached. The clad outside temperature remains close to the saturation temperature. As a result, Zircaloy oxidation is not,
37 CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS 38
therefore, an issue. • A ramp change in boron concentration has lower consequences of boron dilution in comparison to those in a step change. A ramp change means that there is a mixing process in the lower plenum. So, mixing should be a very effective inherent protective mechanism. • The extent of severity of boron dilution transients obviously depends on what kind of boron concentration spatial distribution results during the mixing process in the downcomers and the core inlet plenum, as well as on how much boron dilution amounts to. Poor mixing may lead to a much larger hot channel factor. • The axial power shifts swiftly with advancement of the diluted slug. The maximum power occures in the lower half of the core. This is because the coolant is still subcooled near the core inlet while much void may be produced near the core outlet which limits the increase in power by supplying a void or moderator density reactivity feedback. • The enthalpy deposition in fuel is a function of the burnup of assemblies and its position in the core. It does not take much dilution to insert significant amount of energy into fuel. • The fresh fuel power increase is substantially greater than that for the spent fuel, and also the enthalpy deposited in fresh fuel is about 30% larger than that deposited in the spent fuel. • The cladding temperature does not reach the safety limit (1270K) in all the cases analyzed, whereby the zircaloy oxidation potential is low.
5.2 Recommendations
The following recommendations are made for the future work:
• Mixing phenomena should be analyzed with a 3D fluid dynamics code, and the code should be validated against the data from Alvkarleby and from other sources, e.g., proposed benchmark experiments. • An analysis of effects of cross flow and possible flow reversal, in case of CHF, should be carried out because the flow rate is generally small during boron dilution tran- sients while there is substantial energy production owing to insertion of a relatively large reactivity into the core. • Natural circulation scenarios should be studied. CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS 39
• Coupled mixing in the loop and the core neutronics analysis should be performed.
• A model for pin power reconstruction should be incorporated into the ARROTTA code so as to study the behavior of the hottest pin, calculate DNB as well as local power peaking factors. Bibliography
[1] S. Salah, C.E. Rossi, and J.M. Geets, "Three-Dimensional Kinetic Analysis of an Asymmetric Boron Dilution in a PWR Core," Trans. Amer. Nucl. Soc, 15, Novem- ber, 1972.
[2] E.W. Hagen, "Evaluation of Events Involving Unplanned Boron Dilution Loop, " NUREG/CR-2798, Oak Ridge National Laboratory, July, 1982.
[3] S. Jacobson, "Some of Local Dilution Transients in a Pressurized Water Reactor," Linkoping University, Studies in Science and Technology, Thesis No. 171, 1989.
[4] S. Jacobson, "Risk Evaluation of Local Dilution Transients in a Pressurized Water Reactor," Linkoping University, Studies in Science and Technology, Dissertation No. 272, 1992.
[5] J. Hyvarinen, "The Inherent Boron Dilution Mechanism in Pressurized Water Re- actor," Nuclear Engineering and Design, 145, p.p. 227-240, 1993. [6] D.J. Diamond, P. Kohut, H. Nourbakhsh, K. Valtonen and P. Seeker, "Probabil- ity and Consequences of Rapid Boron Dilution in a PWR," BNL-NUREG-52313, Brookhaven National Laboratory. [7] H. Tuomisto, "Perspectives of Boron Dilution," OECD/CSNI Specialist Meeting on Boron Dilution Reactivity Transients, State College, Pennsylvania, USA, 18-20, October, 1995.
[8] H. Nourbakhsh and Z. Cheng, "Potential for Boron Dilution During Small Break LOCAs in PWRs," Department of Advanced Technology, Brookhaven National Lab- oratory, October, 1994.
[9] K. Haule, J. Hyvarinen, "Potential Reactivity Problems Caused by Boron Separa- tion/Dilution During Partial Loss of Inventory Transients and Accidents in PWRs, " STUK/YTO Memo, N November 12, 1991.
[10] J.G. Sun, W.T. Sha, "Analysis of Thermal Mixing and Boorn Dilution in a PWR," ANL-91/43, Argonne National Laboratory, February, 1993.
40 BIBLIOGRAPHY 41
[11] J.G. Sun, W.T. Sha, "Analysis of Boron Dilution in a Four-loop PWR," ANL-94/35, Argonne National Laboratory.
[12] Los Alamos National Laboratory Safety Code Development Group, "TRAC- PF1/M0D1: An Advanced Best-Estimate Computer Program for Pressurized Re- actor Thermal-Hydraulic Analysis," Volume I: Users Manual, NUREG/CR-2896, 1983.
[13] D. Van Essen, D. Kirkcaldy, P.J. Pheps, "PHOENICS code Thermal Hydraulic Anal- ysis of the SNR-300 IHX," CHAM Internal Report No 1985/23, Wimbledon, London, Englland, 1985.
[14] W.T. Sha, H.M. Domanus, R.C. Dchmitt, J.J. Lin, COMMIX-1: A Three- Dimensional Transient Single-Phase Component Computer Program for Thermal- Hydraulic Analysis, NUREG/CR-0785, ANL-77-96, Sept., 1978.
[15] L.D. Eisenhart, "ARROTTA-01-An Advanced Rapid Reactor Operational Transient Analysis Computer Code," NP-7375-CCML, EPRI, June, 1991.
[16] H. Tinoco, B. Hemstrom and N.G. Andersson, "Physical Modelling of a Rapid Boron Dilution Transient, the EDF Case," Report No. VU-S 94:B16, Vattenfall Utveckling AB, 1994. [17] P.H. Huang, K.Y: Peng, W.C. Lin and J.Y. Wu, "Qulification of ARROTTA CODE for LWR Accident Analysis," The 4th International Topical Meeting on Nuclear Thermal Hydraulic Operations and Safety, April 6-8, 1994, Taipei, Taiwan.
[18] M. Edenius, K. Ekberg, B.H. Forssen, D. Knott, The User's Manual of CASMO-4-A Fuel Assembly Burnup Program, Studsvik/SOA-93/1. Appendix A
Results for Case 1
1300
OH 1200 i ! z t i o i ! Plane 2 Plane 13 - i < _ 1100 i ! Plane 25 i i i ; U 1000 z uo 900 0 6 9 12 15 TIME (s)
Figure A.I: Change in boron concentration as a function of time for Case 1
42 APPENDIX A. RESULTS FOR CASE 1 43
P u <
6 9 15 TIME (s)
Figure A.2: Core reactivity as a function of time for Case 1
100000
6 9 12 15 TIME (s)
Figure A.3: Total core power as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 44
1200
200 6 9 TIME (s)
Figure A.4: Core peak fuel temperature as a function of time for Case 1
90
75 "j u 60 h- / •
Position (1,1) - Z - •-•-- Position (4,1) w Position (6,1) :.. _J - 30 6 9 12 15 TIME (s)
Figure A.5: Fuel enthalpy of Plane 2 as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 45
120 > i | r 1 | I
105
— 90 u 75 ; // .--••
'• /'/
60 •- //.•• Position (1,1) Position (4,1) 45 [U Position (6,1) i i 30 1 i . l . I i . I 6 9 12 15 TIME (s)
Figure A.6: Fuel enthalpy of Plane 13 as a function of time for Case 1
70 ' ' I ' ' I •
• S60 U : //
; // 4 E Position (1,1) 40 --•• Position (4,1) - m Position (6,1)
30 i . , i . i . . i 6 9 12 15 TIME (s)
Figure A.7: Fuel enthalpy of Plane 25 as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 46
10000.0
1000.0
100.0
10.0 Position (1,1) 1.0 Position (4,1) Position (6,1) 0.1
0.0 0 6 9 12 15 TIME (s)
Figure A.8: Nodal power of Plane 2 as a function of time for Case 1
10000.0 1000.0 - U : 100.0
10.0 Position (1,1) 1.0 Position (4,1) -= Position (6,1) 0.1 ! 0.0 0 6 9 12 15 TIME (s)
Figure A.9: Nodal power of Plane 13 as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 47
1000.0 r
100.0
10.0
1.0 Position (1,1) O Position (4,1) 0- 0.1 Position (6,1)
0.0 0 6 9 12 15 TIME (s)
Figure A.10: Nodal power of Plane 25 as a function of time for Case 1
750.0 ' 1 ' ' 1 ' • 1 ' '
- U 650.0
550.0 -
*" •" " " - •••• - • - -- -
5; //' •• a 450.0 - a. Position (1,1) Position (4,1) I Position (6,1) H 350.0 , J 250.0 i i 1 i . . i , i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure A.ll: Fuel temperature of Plane 2 as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 48
850.0
_ 750.0 : u g 650.0 550.0
450.0 Position (1,1) w Position (4,1) 350.0 Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure A. 12: Fuel temperature of Plane 13 as a function of time for Case 1
550.0
500.0 b
Position (1,1) Position (4,1) Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure A. 13: Fuel temperature of Plane 25 as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 49
320.0
u 310.0 :
300.0 -
Position (1,1) 290.0 Position (4,1) Position (6,1) 280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure A.14: Clad outside temperature of Plane 2 as a function of time for Case 1
360.0
•
340.0 / B - < 320.0 i f Position (1,1) 300.0 - Position (4,1) - • 1 Position (6,1) 280.0 i 1 i . , i i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure A. 15: Clad outside temperature of Plane 13 as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 50
360.0 1 1 | r I - p T- • T , --I— -r - | -i 1
340.0
• - - - -... , ...--....-- - -•
<; 320.0 ; /
Position (1,1)
300.0 - Position (4,1) - '•I Position (6,1)
280.0 \ > • > i . • i i i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure A.16: Clad outside temperature of Plane 25 as a function of time for Case 1
VOID FRACTION
22 TIME(s) IS 20 14 16 AXIAL PLANE
Figure A. 17: Axial void fraction distribution as a function of time for Case 1 APPENDIX A. RESULTS FOR CASE 1 51
RELATIVE POWER
15 AXIAL PLANE
Figure A. 18: Axial power distribution as a function of time for Case 1 Appendix B
Results for Case 2
1300
1200 I- i I Plane 2 1100 Plane 13 Plane 25 H 1000
900 o u 800 0 6 9 12 15 TIME (s)
Figure B.I: Change in boron concentration as a function of time for Case 2
52 APPENDIX B. RESULTS FOR CASE 2 53
100000 F
Pi W I PL,
Figure B.2: Total core power as a function of time for Case 2
2.00
6 9 12 15 TIME (s)
Figure B.3: Core reactivity as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 54
1600
u
6 9 12 15 TIME (s)
Figure B.4: Core peak fuel temperature as a function of time for Case 2
100000.0 10000.0 1000.0
100.0 r 04 10.0 r Position (1,1) 1.0 Position (4,1) Position (6,1) 0.1 0.0 0 6 9 12 15 TIME (s)
Figure B.5: Nodal power of Plane 2 as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 55
10000.0
1000.0 r
100.0 r ' \ 10.0 - i Position (1,1) O 1.0 Position (4,1) OH Position (6,1) 0.1
0.0 6 9 12 15 TIME (s)
Figure B.6: Nodal power of Plane 13 as a function of time for Case 2
10000.0
1000.0 r
100.0
10.0 Position (1,1) O 1.0 Position (4,1) OH Position (6,1) 0.1
0.0 6 9 12 15 TIME (s)
Figure B.7: Nodal power of Plane 25 as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 56
120
105 O 90 u fc 75
60 Position (1,1) Position (4,1) 45 Position (6,1) 30 0 6 9 12 15 TIME (s)
Figure B.8: Fuel enthalpy of Plane 2 as a function of time for Case 2
105
s 90 75 //
60 Position (1,1) JTHALP Y Position (4,1) w 45 Position (6,1)
30 6 9 12 15 TIME (s)
Figure B.9: Fuel enthalpy of Plane 13 as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 57
60
P < 50 h u
X 40 Position (1,1) H Position (4,1) Position (6,1)
30 0 6 9 12 15 TIME (s)
Figure B.10: Fuel enthalpy of Plane 25 as a function of time for Case 2
1000.0
u g 750.0 -- - - _ _ < w OH 500.0 - Position (1,1) Position (4,1) - i Position (6,1) . 250.0 I . . ] , I i • 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure B.ll: Fuel temperature of Plane 2 as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 58
750.0
u 650.0
a 550.0
450.0 Position (1,1) Position (4,1) 350.0 Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure B.12: Fuel temperature of Plane 13 as a function of time for Case 2
500.0
450.0 - u
400.0
W 350.0 Position (1,1) OH Position (4,1) g Position (6,1) H 300.0 250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure B.13: Fuel temperature of Plane 25 as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 59
330.0
320.0 \- u 310.0
g 300.0 Position (1,1) Position (4,1) H 290.0 Position (6,1)
280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure B.14: Clad outside temperature of Plane 2 as a function of time for Case 2
360.0
Position (1,1) Position (4,1) Position (6,1) 280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure B.15: Clad outside temperature of Plane 13 as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 60
ODU.U
•
340.0 -
•••• - •------•• - - •• - - •• ~ -•
320.0 -
rosition (.1,1) 300.0 - Position (4,1) Position (6,1)
oan n i 1 . . I . . I , i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure B.16: Clad outside temperature of Plane 25 as a function of time for Case 2
VOID FRACTION
TIME(s)
AXIAL PLANE
Figure B.17: Axial void fraction distribution as a function of time for Case 2 APPENDIX B. RESULTS FOR CASE 2 61
RELATIVE POWER
15 AXIAL PLANE 12
TIME (s)
Figure B.18: Axial power distribution as a function of time for Case 2 Appendix C
Results for Case 3
1300 1 ' ' ( 1 , 1 1200 1 1 - 1100 i 1 1 1 Plane 2 0 ; i 1000 • Plane 13 - 900 ; i Plane 25 i i 1 uw 800 i 700 - uo 600 i . . i . . i . . i 6 9 12 15 TIME (s)
Figure C.I: Change in boron concentration as a function of time for Case 3
62 APPENDIX C. RESULTS FOR CASE 3 63
100000
04
6 9 12 15 TIME (s)
Figure C.2: Total core power as a function of time for Case 3
U < a
6 9 12 15 TIME (s)
Figure C.3: Core reactivity as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 64
o 6 9 15 TIME (s)
Figure C.4: Core peak fuel temperature as a function of time for Case 3
100000.0 10000.0 |n 1000.0 100.0
10.0 Position (1,1) 1.0 Position (4,1) : t Position (6,1) 0.1 0.0 0 6 9 12 15 TIME (s)
Figure C.5: Nodal power of Plane 2 as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 65
10000.0
1000.0 K 100.0 :
10.0 - Position (1,1) 1.0 Position (4,1) L, Position (6,1) 0.1 } 0.0 6 9 12 15 TIME (s)
Figure C.6: Nodal power of Plane 13 as a function of time for Case 3
10000.0
1000.0
100.0
OH 10.0 Position (1,1) 2 1.0 Position (4,1) u Position (6,1) 0.1
0.0 0 6 9 12 15 TIME (s)
Figure C.7: Nodal power of Plane 25 as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 66
150 r\__' : O 120 - u £ 90 Position (1,1) E 60 - Position (4,1) - Position (6,1) 30 i , . i 0 6 9 12 15 TIME (s)
Figure C.8: Fuel enthalpy of Plane 2 as a function of time for Case 3
750.0
650.0 - u
550.0 [
& 450.0 Position (1,1) Position (4,1) 350.0 Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.9: Fuel enthalpy of Plane 13 as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 67
60
55 f-
50 3u 45 / —
40 F Position (1,1) Position (4,1) 35 Position (6,1)
30 6 9 12 15 TIME (s)
Figure C.10: Fuel enthalpy of Plane 25 as a function of time for Case 3
1250.0
1050.0 \-
850.0
650.0 PK - Position (1,1) 450.0 Position (4,1) Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.ll: Fuel temperature of Plane 2 as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 68
750.0
650.0 - u
550.0 -
W 450.0 h Position (1,1) Position (4,1) B 350.0 Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.12: Fuel temperature of Plane 13 as a function of time for Case 3
450.0
400.0 - - -
350.0 - - •' "• " " , I 1 t . Position (1,1) | 300.0 Position (4,1) - Position (6,1)
250.0 • 1 I 1 • i ! • 1 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.13: Fuel temperature of Plane 25 as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 69
350.0 340.0 U 330.0 320.0 310.0 300.0 Position (1,1) Position (4,1) 290.0 Position (6,1) 280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.14: Clad outside temperature of Plane 2 as a function of time for Case 3
360.0
340.0
320.0
Position (1,1) g 300.0 Position (4,1) Position (6,1)
280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.15: Clad outside temperature of Plane 13 as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 70
360.0
•
340.0 f -.. - •••• - - -: / - - " " - " 1 320.0 04 I
! : Position (1,1)
300.0 - / Position (4,1) - / / Position (6,1) /,
280.0 1 i . , i I 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure C.16: Clad outside temperature of Plane 25 as a function of time for Case 3
VOID FRACTION
TIME(s)
AXIAL, PLANE
Figure C.17: Axial void fraction distribution as a function of time for Case 3 APPENDIX C. RESULTS FOR CASE 3 71
RELATIVE POWER
11 15 AXIAL PLANE 12
TIME (s)
Figure C.18: Axial power distribution as a function of time for Case 3 Appendix D
Results for Case 4
1300 1 , 1 ' 1200 1 1 - 1100 ; i Plane 2 o ; i 1000 Plane 13 - < : i 900 i Plane 25 i i W 800 ! i - > i
u 1 ' • o 700 u . • 600 0 6 9 12 15 TIME (s)
Figure D.I: Change in boron concentration as a function of time for Case 4
72 APPENDIX D. RESULTS FOR CASE 4 73
100000
I
Figure D.2: Total core power as a function of time for Case 4
u i
6 9 12 15 TIME (s)
Figure D.3: Core reactivity as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 74
2000
u
200 6 9 12 15 TIME (s)
Figure D.4: Core peak fuel temperature as a function of time for Case 4
100000.0 10000.0 1000.0 r 100.0 r
10.0 Position (1,1) 1.0 Position (4,1) Position (6,1) 0.1 0.0 0 12 15 TIME (s)
Figure D.5: Nodal power of Plane 2 as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 75
10000.0 F
1000.0 r
2 Position (1,1) Position (4,1) Position (6,1)
6 9 12 15 TIME (s)
Figure D.6: Nodal power of Plane 13 as a function of time for Case 4
10000.0
1000.0
O ft* Position (1,1) Position (4,1) Position (6,1)
6 9 12 15 TIME (s)
Figure D.7: Nodal power of Plane 25 as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 76
1500.0
1250.0 - u 1000.0 5 8 750.0 O-i Position (1,1) Position (4,1) H 500.0 Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.8: Fuel enthalpy of Plane 2 as a function of time for Case 4
650.0
550.0
450.0
s Position (1,1) 350.0 Position (4,1) Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.9: Fuel enthalpy of Plane 13 as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 77
55
50 h
£
30 6 9 12 15 TIME (s)
Figure D.10: Fuel enthalpy of Plane 25 as a function of time for Case 4
1500.0
U 1250.0
1000.0
W 750.0 Position (1,1) 500.0 Position (4,1) Position (6,1) 250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.ll: Fuel temperature of Plane 2 as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 78
650.0
5 550.0
< 450.0 . w i Position (1,1) H 350.0 Position (4,1) • Position (6,1)
250.0 i i . . i . . i . 0.0 3.0 6.0 9.0 12.0 15.0 TIME(s)
Figure D.12: Fuel temperature of Plane 13 as a function of time for Case 4
450.0
400.0
< 350.0 wai OH Position (1,1) S 300.0 Position (4,1) Position (6,1)
250.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.13: Fuel temperature of Plane 25 as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 79
360.0
6 340.0
320.0
Position (1,1) 300.0 Position (4,1) Position (6,1)
280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.14: Clad outside temperature of Plane 2 as a function of time for Case 4
360.0
B 340.0 h
< 320.0
OH Position (1,1) m 300.0 Position (4,1) Position (6,1)
280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.15: Clad outside temperature of Plane 13 as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 80
360.0 11 t '
: I 340.0 ; - i
320.0 - - i
06 1 W • i ' rosition (,i,ij r - 300.0 -r 1 Position (4,1) - Position (6,1) - 280.0 i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure D.16: Clad outside temperature of Plane 25 as a function of time for Case 4
VOID FRACTION
24 26 TIME (s) 20 16 18
AXIAL PLANE
Figure D.17: Axial void fraction distribution as a function of time for Case 4 APPENDIX D. RESULTS FOR CASE 4 81
RELATIVE POWER
11 15 AXIAL PLANE
TIME (s)
Figure D.18: Axial power distribution as a function of time for Case 4 Appendix E
Results for Case 5
1300 • 1 I 1 • 1 1
1 • - -1 1 1 Q_ 1200 - I 1 1 1 1 1 0 Plane 2 ! i Plane 13 i ' _ rr 1100 - ' i Plane 25 i- LJJ o 1000 -- z o o 900 i , , i , . i , , i 0 6 9 12 15 TIME (s)
Figure E.I: Change in boron concentration as a function of time for Case 5
82 APPENDIX E. RESULTS FOR CASE 5 83
1300 < 1 I • 1 1 I ' '
1 1 I t Q- 1200 I 1
1 Plane 2 Q 1100 - - i - 1 Plane 13 1 Plane 25 _ 1000 - 1 111 o 1 900 -
800 1 . . I . . I . , I , , 0 6 9 12 15 TIME (s)
Figure E.2: Change in boron concentration as a function of time for Case 5
10000.0
1000.0 r 100.0 - k I 10.0 Position (1,1) 1.0 Position (4,1) - Position (6,1) 0.1
0.0 6 9 12 15 TIME(s)
Figure E.3: Nodal power of Plane 2 as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 84
10000.0
1000.0 100.0 - rx ! 10.0 - Position (1,1) 2 1.0 Position (4,1) - Position (6,1) 0.1
0.0 0 6 9 12 15 TIME (s)
Figure E.4: Nodal power of Plane 13 as a function of time for Case 5
1000.0
100.0 i
10.0 -
1.0 Position (1,1) o Position (4,1) CL, 0.1 Position (6,1)
0.0 6 9 12 15 TIME (s)
Figure E.5: Nodal power of Plane 25 as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 85
100 i 1 i • 1 . 90 80 _: 70 60 Position (1,1) 50 : Z, Position (4,1) w 40 Position (6,1) : i 30 I . . I i 6 9 12 15 TIME (s)
Figure E.6: Fuel enthalpy of Plane 2 as a function of time for Case 5
110 100 O 90 80 // / 70 60 /•••• Position (1,1) 50 li; — Position (4,1) 40 Position (6,1) 30 6 9 12 15 TIME (s)
Figure E.7: Fuel enthalpy of Plane 13 as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 86
70
Position (1,1) Position (4,1) Position (6,1)
6 9 12 15 TIME (s)
Figure E.8: Fuel enthalpy of Plane 25 as a function of time for Case 5
800.0
_, 700.0 - - u g 600.0
/ ,- ••• --•••• -
- " " ••• ""• - •• ------500.0 w
• Position (1,1) 400.0 - - Position (4,1) I 300.0 _ _ Position (6,1)
• 200.0 i i • . i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure E.9: Fuel temperature of Plane 2 as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 87
900.0 800.0 U 700.0 600.0 500.0 Position (1,1) 400.0 Position (4,1) 300.0 = I Position (6,1) 200.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure E.10: Fuel temperature of Plane 13 as a function of time for Case 5
500.0
•
U
•'•" " " - 400.0 • F - -—-• - - •• gj 300.0 Position (1,1) Position (4,1) - Position (6,1)
200.0 i i i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure E.ll: Fuel temperature of Plane 25 as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 88
320.0 ••I- | r . 1- •—T r 1 1 1
310.0 -
< 300.0 - •---..... -
i Position (1,1) - S 290.0 Position (4,1) ^ Position (6,1)
• 280.0 i - I , , L i • i . i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure E.12: Clad outside temperature of Plane 2 as a function of time for Case 5
360.0 350.0 340.0 - 330.0 URE( C 320.0 - 310.0 OH Position (1,1) 300.0 Position (4,1) 290.0 Position (6,1) 280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure E.13: Clad outside temperature of Plane 13 as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 89
360.0
Position (1,1) Position (4,1) Position (6,1)
280.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME(s)
Figure E.14: Clad outside temperature of Plane 25 as a function of time for Case 5
VOID FRACTION
TIME(s)
AXIAL PLANE
Figure E.15: Axial void fraction distribution as a function of time for Case 5 APPENDIX E. RESULTS FOR CASE 5 90
RELATIVE POWER
IS AXIAL PLANE ls 12
TIME (s)
Figure E.16: Axial power distribution as a function of time for Case 5 Appendix F
Results for Case 6
1300 i , | i i | T
1200 - \ \ \ O Plane 2 \ ^ \ Plane 13 < 1100 - \ ^ x Plane 25 I- \ N- s\ LU 1000 o o 900 , 1 , . 1 , , 1 , , 1 , , 0 6 9 12 15 TIME (s)
Figure F.I: Change in boron concentration as a function of time for Case 6
91 APPENDIX F. RESULTS FOR CASE 6 92
1300
1200 ^\ \ \ - (P P : \ \ \ z Plane 2 O 1100 • \ \ x -
x Plane 13 l- \ ^
QC : \ ^ \ Plane 25
1- 1000 \ \ \
\ \ - 111 O z 900 : \ \ x\. o 800 0 6 9 12 15 TIME (s)
Figure F.2: Change in boron concentration as a function of time for Case 6
1000.0
100.0
10.0 _ -
1.0 Position (1,1) 2 Position (4,1) 1 Position (6,1) 0.1
0.0 0 6 9 12 15 TIME (s)
Figure F.3: Nodal power of Plane 2 as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 93
10000.0 3
1000.0 -
100.0 : 10.0 : I rosmon (.1,1) 1.0 g Position (4,1) Position (6,1) 0.1 ! 0.0 6 9 12 15 TIME (s)
Figure F.4: Nodal power of Plane 13 as a function of time for Case 6
10000.0
1000.0 - -
100.0
10.0 -: •• I r osition (,i,ij 1.0 Position (4,1) -=_ Position (6,1) 0.1 | 0.0 6 9 12 15 TIME (s)
Figure F.5: Nodal power of Plane 25 as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 94
90
80 CD 3 70
60
ffi 50 Position (1,1) Position (4,1) w 40 Position (6,1) 30 0 6 9 12 15 TIME (s)
Figure F.6: Fuel enthalpy of Plane 2 as a function of time for Case 6
120 110 : 100 : 90 r u 80 70 a 60 Position (1,1) w 50 Position (4,1) 40 Position (6,1) 30 0 6 9 12 15 TIME (s)
Figure F.7: Fuel enthalpy of Plane 13 as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 95
80
p 70 - "---._ ; U 60 : / 50 Position (1,1) Position (4,1) 40 Position (6,1) • J I.I.II I 30 1 1 1 I . , 1 1 . 1 0 6 9 12 15 TIME (s)
Figure F.8: Fuel enthalpy of Plane 25 as a function of time for Case 6
700.0
• 600.0
b 500.0 -
g 400.0 Position (1,1) Position (4,1) H 300.0 L - L J Position (6,1)
• 200.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure F.9: Fuel temperature of Plane 2 as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 96
900.0
800.0 - u 700.0 : w
600.0 / / . •- '" - ~ • •• - -. - - - < 500.0 Position (1,1) 400.0 Position (4,1)
300.0 Position (6,1) i,,, , i,,
200.0 1 , , 1 . , 1 , , 1 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure F.10: Fuel temperature of Plane 13 as a function of time for Case 6
600.0
5 500.0 -
< 400.0 -
Position (1,1) W 300.0 Position (4,1) H Position (6,1)
200.0 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure F.ll: Fuel temperature of Plane 25 as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 97
310.0 1 1 • I 1 1 1 1 1 •
U
300.0 -
Position (1,1) 290.0 - / Position (4,1) • Position (6,1)
1 280.0 1 . 1 1 • • 1 i ! 1 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure F.12: Clad outside temperature of Plane 2 as a function of time for Case 6
360.0 I 1 I 1 -
6 340.0
< 320.0 -
£ Position (1,1) m 300.0 h Position (4,1) - / Position (6,1)
•. / 280.0 1 i . . i i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure F.13: Clad outside temperature of Plane 13 as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 98
360.0 1 1 1 1
-
S 340.0 w - - •• - :
< 320.0 /
Position (1,1)
300.0 - // Position (4,1) - Position (6,1)
280.0 1 , . 1 , . 1 , i 0.0 3.0 6.0 9.0 12.0 15.0 TIME (s)
Figure F.14: Clad outside temperature of Plane 25 as a function of time for Case 6
VOID FRACTION
26 22 24 TIME Figure F.15: Axial void fraction distribution as a function of time for Case 6 APPENDIX F. RESULTS FOR CASE 6 99 RELATIVE POWER 1.55 - 1.05 - 0.55 - 15 AXIAL PLANE 12 TIME (s) Figure F.16: Axial power distribution as a function of time for Case 6 Appendix G Results for Case 7 1 .Oe+00 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.I: Total core power as a function of time for Case 7 100 APPENDIX G. RESULTS FOR CASE 7 101 u -1.50 0 5 10 15 20 25 30 35 40 45 50 TIME(s) Figure G.2: Core reactivity as a function of time for Case 7 1250 •—• u 250 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.3: Core peak fuel temperature as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 102 1.0e+04 r- I 1 T--J I I I I J—T-T-I—T ^ 1 1I I" ( 1.0e+03 - Position (1,9) Position (4,9) 1 .Oe+02 Position (6,9) w 1 .Oe+01 1 .Oe+00 i , , . , i . . , . i . , . . i . , , , i . . , . i . , , . rr -r 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.4: Nodal power of Plane 2 as a function of time for Case 7 1 .Oe+04 ' • I l....i..l_^_l— 1 .Oe+03 Position (1,9) ; Position (4,9) 25, 1.Oe+02 t- \ Position (6,9) O ex 1.0e+01 1 0e+00 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.5: Nodal power of Plane 13 as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 103 1.0e+04 r— 1 .Oe+03 1 .Oe+02 Position (1,9) Position (4,9) Position (6,9) s 1.0e+01 1 .Oe+00 1 .Oe-01 1.0e-02 L i , , , • I • , . • I • , • • i i i l i , , , l 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.6: Nodal power of Plane 25 as a function of time for Case 7 100 r O 80 Position (1,9) U Position (4,9) Position (6,9) 60 40 w 20 I . i , , 1 | , | , I 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.7: Fuel enthalpy of Plane 2 as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 104 120 100 (- - Position (1,9) - Position (4,9) y so Position (6,9) OH 3 60 § 40 - 20 ] . . . . | . 1 | 1 | , , 1 , | . . , . | | 1 . . | » ! , . | , . , , | 0 5 10 15 20 25 30 35 40 45 50 TIME(s) Figure G.8: Fuel enthalpy of Plane 13 as a function of time for Case 7 70 . . . | . . i i | . . . . | . . . i [ i i Position (1,10) 60 Position (4,10) - I Position (6,10) u 50 - 40 - 30 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.9: Fuel enthalpy of Plane 25 as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 105 850 I ' ' " ' i r ' ' ' I ' ' ' ' I ' 750 - Position (1,9) Position (4,9) 650 - Position (6,9) 550 450 350 250 ,.!..• I ,•,., I ..!, I ,••.••,,,,.,,, 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.10: Fuel temperature of Plane 2 as a function of time for Case 7 850 ^ 750 Position (1,9) Position (4,9) y Position (6,9) g 650 - < 550 oi 450 350 250 r .. i, , , . i i ... i ,.. . i. i i 11 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.ll: Fuel temperature of Plane 13 as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 106 500 Position (1,9) 450 U Position (4,9) Position (6,9) p 400 350 300 250 i , , , , i » i , , i . . . , i 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.12: Fuel temperature of Plane 25 as a function of time for Case 7 320 Position (1,9) 310 Position (4,9) Position (6,9) 300 h 290 280 i i . , , i 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.13: Clad outside temperature of Plane 2 as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 107 360 B 340 - Position (1,9) Position (4,9) 5 320 Position (6,9) Pi u 300 280 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.14: Clad outside temperature of Plane 13 as a function of time for Case 7 360 i 340 Position (1,9) Position (4,9) 320 Position (6,9) S 300 280 >-— , i.... i..,. i,., . i 0 5 10 15 20 25 30 35 40 45 50 TIME (s) Figure G.15: Clad outside temperature of Plane 25 as a function of time for Case 7 APPENDIX G. RESULTS FOR CASE 7 108 VOID FRACTION AXIAL PLANE 10 15 10 20 30 25 40 35 TIME (s) Figure G.16: Axial void fraction distribution as a function of time for Case 7 RELATIVE POWER 50 40 45 AXIAL PLANE '5 35 25 30 20 10 15 TIME (s) Figure G.17: Axial power distribution as a function of time for Case 7 Appendix H The EXPICKER file C - THIS SMALL PROGRAM PREPARES A BINARY FILE TO BE READ C - BY REBLEND AS IF IT WERE COMING FROM A SIMULATE CAL- CULATION. C - AN IMAGINARY PWR CORE IS BEING REPRESENTED HERE. C - DIMENSION STATEMENT FOR VARIABLES THAT C - DESCRIBE THE CORE OR THE PROBLEM DIMENSION ITITLE(21), JMN(34), JMX(34), B(100,50), & NFT(34,34), CONC(3,34,34,34),JMN1(34),JMX1(34) C - DIMENSION STATEMENT FOR INTERNAL VARIABLES DIMENSION LPI(20,3) CHARACTER*4 BLANK C - INITIALIZING VARIABLES THAT DESCRIBE THE CORE OR THE PROBLEM DATA ITITLE /' ', ' ', 'THIS',' IS ', 'THE ', TITL', 'E !!', 1 13*' ',' '/ DATA CONC /117912*1./ ID = 9 JD = 9 KD = 26 ISET2 = 1 DZ = 396.24/26 C describing the core radially DO 10 I=1,ID JMN(I) = 1 JMX(I) = 9 IF(I .EQ. 4) JMX(I) = 8 IF(I .EQ. 5) JMX(I) = 8 IF(I .EQ. 6) JMX(I) = 7 109 APPENDIX H. THE EXPICKER FILE 110 IF(I .EQ. 7) JMX(I) = 6 IF(I .EQ. 8) JMX(I) = 5 IF(I .EQ. 9) JMX(I) = 3 10 CONTINUE DO 11 I=1,ID-1 JMN1(I) = 1 JMX1(I) = 8 IF(I .EQ. 3) JMX1(I) = 7 IF(I .EQ. 4) JMX1(I) = 7 IF(I .EQ. 5) JMX1(I) = 6 IF(I .EQ. 6) JMX1(I) = 5 IF(I .EQ. 7) JMX1(I) = 4 IF(I .EQ. 8) JMX1(I) = 2 11 CONTINUE READ(ll,100) READ(ll,100) READ(ll,100) DO 12 I=1,ID READ(ll,100) (NFT(I,J),J=JMN(I),JMX(I)) 100 FORMAT(8X,9I5) 12 CONTINUE C describing the assembly types axially DO 15 NF=9,28 B(10,NF) = FLOAT(29) B(11,NF) = DZ B(12,NF) = FLOAT(NF) B(13,NF) = 396.24-DZ B(14,NF) = FLOAT(30) B(15,NF) = 396.24 15 CONTINUE C preparing the history matrix DO 20 I=1,ID DO 20 K=1,KD DO 20 J=1,JD CONC(2,J,K,I) = 0.0 20 CONC(1,J,K,I) = 0.752 C prepare the assembly exposure history READ(11,200) READ(ll,200) READ(ll,200) DO 25 I=1,ID READ(11,200) DO 25 K=KD,1,-1 APPENDIX H. THE EXPICKER FILE 111 READ(ll,200) (C0NC(2,J,K,I),J=JMN(I),JMX(I)) 200 FORMAT(2X,9F7.3) 25 CONTINUE C prepare the moderator density history READ(ll,200) READ(11,200) READ(ll,200) DO 35 I=1,ID-1 READ(11,200) DO 35 K=KD,1,-1 READ(ll,200) (CONC(1,J,K,I),J=JMN1(I),JMX1(I)) 35 CONTINUE C for the biginning of reactor lifetime C do 26 i=l,id C do 26 k=kd,l,-l C do 26 j=jmn(i),jmx(i) C 26 conc(2,j,k,i) = 0. C - INITIALIZING INTERNAL VARIABLES DUMMY = -777. BLANK = ' ' IZERO = 0 IONE = 1 RZERO = 0. RONE = 1. LENGT5 = 5450 RDATA1 = 1./0.016018 ND = 3-ISET2 DO 30 1=1,20 DO 30 J=l,3 30 LPI(I,J) = 0 LPI(8,1) = 1 C write to a binary file for REBLEND reading C - WRITE RECORD 1 WRITE(l) ITITLE, (DUMMY, 1=1,5), LENGT5 C C - WRITE RECORD 2 WRITE(l) ID, JD, KD, IZERO, ISET2, ND, (DUMMY, 1=1,314), LPI, 1 DUMMY, BLANK, BLANK, IZERO, IZERO, IZERO, 2 (DUMMY, 1=1,18), IONE, (DUMMY, 1=1,32), JMN, JMX C C - WRITE RECORD 3 WRITE(l) DUMMY, JD C APPENDIX H. THE EXPICKER FILE 112 C - WRITE RECORD 4 WRITE(l) DUMMY, DUMMY, DZ, (DUMMY, 1=1,19), RZERO, 1 (DUMMY, 1=1,20), RDATA1, RZERO, (DUMMY, 1=1,23), 2 RZERO, (DUMMY, 1=1,10), RZERO C C - WRITE RECORD 5 WRITE(l) (DUMMY, 1=1,21), BLANK, BLANK C C - WRITE RECORD 6 WRITE(l) DUMMY, B, (DUMMY, 1=1,235), RONE C C - WRITE RECORDS 7, 8, 9, 10, AND 11 DO 40 N=l,5 40 WRITE(l) DUMMY C C - WRITE RECORD 12 WRITE(l) ((NFT(I,J), I=1,ID), J=1,JD) C C - WRITE RECORDS 13, 14, 15, 16, 17, AND 18 DO 50 N=l,6 50 WRITE(l) DUMMY C C - WRITE RECORD 19 DO 60 I=1,ID 60 WRITE(l) (((CONC(N,J,K,I), N=1,ND), J=1,JD), K=1,KD) C STOP END Appendix I The AXMOD file C—BEGIN AXMOD SUBROUTINE AXMOD (I, J, K, PPMRAD) DIMENSION FRONT(40,40), Fl(40,40), F2(40,40) DIMENSION PPM1(4O,4O), PPM2(40,40), VELOC(40,40) DIMENSION START(40,40), SLUT(40,40), PPMSKILN(40,40) DIMENSION RST(40,40), RSL(40,40) DIMENSION AVST(40,40,20), CONC(40,40,20), POS(20) DATA ((F1(I,J),I=1,1O),J=1,1O) / -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50/ DATA ((F2(I,J),I=l,10),J=l,10) / -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, -450,-450,-450,-450,-450,-450,-450,-450,-450,-450, 113 APPENDIX I. THE AXMOD FILE 114 -450,-450,-450,-450,-450,-450,-450,-450,-450,-450/ DATA ((RST(I,J),I=l,10),J=l,10) / -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50, -50,-50,-50,-50,-50,-50,-50,-50,-50,-50/ DATA ((RSL(I,J),I=l,10),J=l,10) / -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674, -674,-674,-674,-674,-674,-674,-674,-674,-674,-674/ DATA ((PPM1(I,J),I=1,10),J=1,10) / 1050,1050,900,900,900,900,1050,1050,1050,1050, 1050,1050,900,900,900,900,1050,1050,1050,1050, 1050,1050,900,900,900,1050,1050,1050,1050,1050, 1050,1050,900,900,900,1050,1050,1050,1050,1050, 1050,1050,900,900,1050,1050,1050,1050,1050,1050, 1050,1050,1050,1050,1050,1050,1050,1050,1050,1050, 1050,1050,1050,1050,1050,1050,1050,1050,1050,1050, 1050,1050,1050,1050,1050,1050,1050,1050,1050,1050, 1050,1050,1050,1050,1050,1050,1050,1050,1050,1050, 1050,1050,1050,1050,1050,1050,1050,1050,1050,1050/ DATA ((PPM2(I,J),I=l,10),J=l,10) / 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, APPENDIX I. THE AXMOD FILE 115 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252, 1252,1252,1252,1252,1252,1252,1252,1252,1252,1252/ DATA (((AVST(I,J,N),I=1,17),J=1,9),N=1,15) / 153*-100.0,153*-750.98,153*-936.0,153*-1014, 153*-1092,153*-1248.0,153*-1375.92,153*-1560.0, 153*-1972.0,153*-2184.0,153*-2410.2,153*-2808.0, 153*-3432.0,153*-4680.0,153*-12480.0/ DATA (((CONC(I,J,N),I=1,17),J=1,9),N=1,15) / 153*1252.0,153*1252.0,153*1218.0, 989,1097,1097,1086,1075,1053,1031,997,986, 1019,1053,1053,1064,1086,1097,1097,989, 989,1097,1097,1086,1075,1064,1031,997,986, 997,1019,1031,1064,1086,1097,1097,989, 989,989,1075,1064,1064,1019,975,942,931, 942,964,986,1031,1075,1097,989,989, 989,989,1042,1042,1042,986,896,853,831, 864,887,909,975,1064,1086,989,989, 3*989,1008,1008,1008,975,896,842, 831,842,909,931,975,3*989, 4*989,986,975,909,864,853, 896,953,975,1008,4*989, 5*989,975,931,909,909,953,1008,1031,5*989, 7*989,931,942,986,7*989, 17*989, 989,1097,1097,1086,1075,1053,1031,997,986, 1019,1053,1053,1064,1086,1097,1097,989, 989,1097,1097,1086,1075,1064,1031,997,986, 997,1019,1031,1064,1086,1097,1097,989, 989,989,1075,1064,1064,1019,975,942,931, 942,964,986,1031,1075,1097,989,989, 989,989,1042,1042,1042,986,896,853,831, 864,887,909,975,1064,1086,989,989, 3*989,1008,1008,1008,975,896,842, 831,842,909,931,975,3*989, 4*989,986,975,909,864,853, 896,953,975,1008,4*989, 5*989,975,931,909,909,953,1008,1031,5*989, 7*989,931,942,986,7*989, 17*989, 153*1020.0,153*989.0,153*1014.0,153*1105.0, 153*1161.0,153*1187.0,153*1215.0,153*1241.0, 153*1252.0,153*1252.0/ DATA ((VELOC(I,J),I=1,17),J=1,9) /153*1.56E+2/ APPENDIX I. THE AXMOD FILE 116 C F1(I,J) is the first boron front position at start of C the AR-run for step (cm below core bottom) C F2(I,J) is the second boron front position at start C of the AR-run for step C RST(I,J) is the position for the beginning of C the boron ramp at start of the AR-run C RSL(I,J) is the position for the end of the boron C ramp at start of AR-run C PPM1(I,J) resp. PPM2(I,J) is the new boron concentration. C The latter is only used for step C VELOC(I,J) is the velocity that slug or ramp has (in cm/sec) C AVST(I,J,N) and CONC(I,J,N) changing positions C and concentrations for varying boron C concentration. The first and the second position both C have to have the initial concentration. C For all this is for each flow channel. DZ = 15.24 TYP = 1 C With typ is the type of boron transient C chosen, 0 for step, 1 for ramp, 2 for varying IF (TYP .EQ. 2) GO TO 50 IF (TYP .EQ. 1) GO TO 30 IF (TYP .EQ. 0) GO TO 10 C Nodal boron slug 10 CONTINUE FRONTANT = 1 C By frontant is the number of instant boron C concentration changes that takes place C given, 1 or 2 DO 25 Q = 1,FRONTANT IF (Q .EQ. 1) FRONT(I,J) = F1(I,J) IF (Q .EQ. 2) FRONT(I,J) = F2(I,J) FRONT(I,J) = FRONT(I,J) + TNOW * VELOC(I,J) IF (Q .EQ. 1) PPMNY = PPM1(I,J) IF (Q .EQ. 2) PPMNY = PPM2(I,J) IF (((K-l) * DZ) .GE. FRONT(I,J)) THEN IF (Q .EQ. 1) PPMRAD = PPMRAD IF (Q .EQ. 2) PPMRAD = PPM1(I,J) IF(Q .EQ. 1) KANT= 1 IF (Q .EQ. 2) KANT = 0 GO TO 20 ENDIF IF ((K * DZ) .LT. FRONT(I,J)) THEN APPENDIX I. THE AXMOD FILE 117 PPMRAD = PPMNY KANT = 0 GO TO 20 ELSE PPMRAD = (PPMRAD*(K*DZ-FRONT(I,J))+PPMNY*(FRONT(I,J)- k (K-1)*DZ))/(K*DZ-(K-1)*DZ) IF (Q .EQ. 1) KANT = 1 IF (Q .EQ. 2) KANT = 0 ENDIF 20 IF (KANT .EQ. 1) GO TO 90 25 CONTINUE GO TO 90 C Nodal boron ramp 30 CONTINUE START(I,J) = RST(I,J) + TNOW * VELOC(I,J) SLUT(I,J) = RSL(I,J) + TNOW * VELOC(I,J) PPMSKILN(U) = (PPMRAD-PPM1(I,J))/(RSL(I,J)-RST(I,J)) IF (I .EQ. 3 .AND. J .EQ. 1 .AND. K .LE. 3) THEN WRITE(598,*) K,TNOW,START(I,J),SLUT(I,J) END IF IF (START(I,J) .LE. ((K-1)*DZ)) THEN PPMRAD = PPMRAD GO TO 40 END IF IF (SLUT(I,J) .GE. (K*DZ)) THEN PPMRAD = PPM1(I,J) GO TO 40 ENDIF IF (START(I,J) .LT. (K*DZ)) THEN PPMRAD = (PPMRAD*(K*DZ - START(I,J)) + k (PPMRAD + PPMSKILN(I,J)* k (START(I,J) - (K-1)*DZ)/2)*(START(I,J) - (K-1)*DZ))/ k (K*DZ - (K-1)*DZ) GO TO 40 ENDIF IF (SLUT(I,J) .GT. ((K-1)*DZ)) THEN PPMRAD = (PPM1(I,J)*(SLUT(I,J)-(K-1)*DZ) + (PPM1(I,J) - k PPMSKILN(I,J)*(K*DZ - SLUT(I,J))/2)*(K*DZ - SLUT(I,J)))/ k (K*DZ- (K-1)*DZ) GO TO 40 ENDIF PPMRAD = PPMRAD + PPMSKILN(I,J)*(START(I,J) - K*DZ+DZ/2) 40 CONTINUE APPENDIX I. THE AXMOD FILE 118 GO TO 90 C Varying boron concentration 50 CONTINUE DO N = 1,15 POS(N) = AVST(I,J,N) + VELOC(I,J) * TNOW END DO DO N = 2,15 IF (POS(2) XE. 0) THEN PPMRAD = PPMRAD ELSE IF (POS(N) .LE. ((K-1)*DZ) .AND. POS(N-l) .GE. (K*DZ)) THEN PPMSKILN(I,J) = (CONC(I,J,N-1) - CONC(I,J,N))/ & (POS(N-l) - POS(N)) SKRAP3 = (POS(N-l) - K*DZ + DZ/2) SKILL3 = PPMSKILN(I,J) * SKRAP3 PPMRAD = CONC(I,J,N-1) - SKILL3 END IF IF ((K*DZ) .GT. POS(N) .AND. ((K-1)*DZ) .LT. POS(N)) THEN AVE1 = CONC(I,J,N) + ((CONC(I,J,N-1)-CONC(I,J,N))/ & (POS(N-l)-POS(N))*(K*DZ-POS(N))/2) AVE2 = CONC(I,J,N) - ((CONC(I,J,N)-CONC(I,J,N+1))/ & (POS(N)-POS(N+1))*(POS(N) -(K-l)*DZ)/2) SKRAP1 = K*DZ - POS(N) SKILL1 = SKRAP1/DZ SKRAP2 = POS(N)-((K-1)*DZ) SKILL2 = SKRAP2/DZ PPMRAD = (AVE1*SKILL1) + (AVE2*SKILL2) END IF END IF END DO 90 CONTINUE RETURN END STATENS KARNKRAFTINSPEKTION Swedish Nuclear Power Inspectorate Postadress/Postal address Telefon/Telephone Telefax Telex SKI Nat 08-698 84 00 Nat 08-661 90 86 11961 SWEATOMS S-106 58 STOCKHOLM Int +46 8 698 84 00 Int +46 8 661 90 86