VTT PUBLICATIONS FI9700010 246

Riitta Kyrki-Rajamaki

Three-dimensional reactor dynamics code for VVER type nuclear reactors

VOL 2 8 Ns 0 6 VTT TECHNICAL RESEARCH CENTRE OF FINLAND ESPOO 1995 VTT PUBLICATIONS 246

Three-dimensional reactor dynamics code for VVER type nuclear reactors

Riitta Kyrki-Rajamaki VTT Energy

Dissertation for the degree of Doctor of Technology to be presented with due permission for public examination and debate in Auditorium FI at Helsinki University of Technology (Espoo, Finland) on the 17th of November, 1995, at 12 o'clock noon.

TECHNICAL RESEARCH CENTRE OF FINLAND mxr p&mm \ ESPOO 1995 left g Kyrki-Rajamaki, Riitta. Three-dimensional reactor dynamics code for WER type nuclear reactors. Espoo 1995, Technical Research Centre of Finland, VTT Publications 246. 51 p. + app. 80 p. UDC 621.039:681.3:621.039.4 Keywords nuclear reactors, reactor dynamics, three-dimensional kinetics, HEXTRAN, mathematical models, computer programs, validation, accident analysis, WWER type reactors, hexagonal fuel

ABSTRACT

A three-dimensional reactor dynamics computer code has been developed, validated and applied for transient and accident analyses of VVER type nuclear reactors. This code, HEXTRAN, is a part of the reactor physics and dynamics calculation system of the Technical Research Centre of Finland, VTT. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and the two-phase flow equations of hydraulics. It includes all the experience of VTT from 20 years on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics. The dynamic coupling with the thermal hydraulic system code SMABRE also allows the VVER circuit-modelling experience to be included in the analyses. With HEXTRAN it is possible to make realistic time-dependent analyses starting from the actual core cycle conditions. Methods for making conservative accident analyses with this best-estimate code have also been developed. The usefulness of the three-dimensionality is shown particularly in accidents with asymmetric fission power distribution originating from local neutronic or thermal hydraulic disturbances in the core or cooling circuits. Complicated accidents in which there are strong interactions between neutron kinetics and thermal hydraulics can be reliably analyzed. The new hydraulics solution method PLIM developed at VTT has been applied in HEXTRAN to remove modelling restrictions and to eliminate numerical diffusion and dispersion. The use of PLIM improves accuracy and expands the applicability range of the code. HEXTRAN has been validated against different types of relevant information available, viz. measurements of a test reactor, start-up experiment and other data of a real plant, as well as with calculations of several international benchmark problems and independent code comparisons. HEXTRAN s applicability to calculate VVER-440 and VVER- 1000 type reactors has been demonstrated. Extensive analyses have been carried out with HEXTRAN on both design basis and new types of accidents, e g. RIA, ATWS or local boron dilutions, for the Finnish Loviisa and Hungarian Paks nuclear power plants as well as for the new Russian VVER-91 concept.

3 PREFACE

This work has been carried out at the Technical Research Centre of Finland (VTT). The development and validation work of the new code HEXTRAN has mostly been made with the funding of the Finnish Centre for Radiation and Nuclear Safety (STUK). Many applications have been part of the domestic and international projects of I VO International Ltd (IVO IN). My deepest and dearest thanks are due to our guru of the reactor dynamics calculation system, Dr. Markku Rajamaki, who has given invaluable advice in all the phases of the work. I am thankful to my supervisor, Prof. Rainer Salomaa for his encouragement during the many phases of the preparation of the thesis. I specially want to thank the reactor dynamics group, Hanna Raty, Dr. Timo Vanttola and Thomas Stenius, for the close cooperation in the development, validation, quality management, and application work of the new code. I am also indebted to other colleagues who have participated in the numerous tough VVER applications of the reactor dynamics code system: reactor physicists Markku Anttila, Elja Kaloinen and Teijo Roine, as well as the "SMABRE group" Jaakko Miettinen, Anitta Hamalainen and Sixten Norrman, and to all our staff. Kalevi Haule, Keijo Valtonen and Juhani Hyvarinen from STUK have initiated and motivated many phases of this development work for the safety studies of nuclear reactors, and to them I want to express my sincere thanks. I am grateful to Perth Siltanen and Martti Antila from IVO IN with whom I have worked in fruitful cooperation during many demanding applications. I wish to thank also my Hungarian co-authors from KFKI AEKI, Andras Kereszturi, Margit Telbisz and Andras Gacs, as well as the colleagues from NPP Paks, AEE, OKB Gidropress, and Kurchatov Institute with whom I have had the opportunity to work while applying HEXTRAN. Finally, I thank my children Eerikki, Tapani, Susanna and Vuokko. They have guaranteed that life is full.

Espoo, September 1995 Riitta Kyrki-Rajamaki

4 LIST OF PUBLICATIONS

This thesis is based on the following publications and on the development work of the HEXTRAN code reported in the summary part: I Kyrki-Rajamaki, R. HEXTRAN: VVER reactor dynamics code for three-dimensional transients. Proceedings of the first Symposium of AER. Rez near Prague 23 - 28 September 1991. Budapest: KFKI Atomic Energy Research Institute, 1991. Pp. 474 - 481. II Kaloinen, E., Anttila, M. & Kyrki-Rajamaki, R. Recent development of VTT’s calculation system for VVERs. Transactions of the ANS Winter Meeting. Washington, DC 13-17 November 1994. La Grange Park, EL: American Nuclear Society, 1994. Pp. 473 - 474. (TANSAO 71 1-692). III Kyrki-Rajamaki, R. & Raty, H. Safety analyses for VVER type reactors with the reactor dynamics calculation system of VTT, Finland. Proceedings of the 1993 Simulation Multiconference. Arlington, VA 29 March - 1 April 1993. San Diego, CA: SCS Simulation Series, 1993. Vol 25, nro 4. Pp. 18 - 23. IV Kyrki-Rajamaki, R Validation of the reactor dynamics code HEXTRAN. Helsinki: Finnish Centre for Radiation and Nuclear Safety, 1994. 24 p. (STUK-YTO-TR 69). V Kyrki-Rajamaki, R Calculation of the first three-dimensional hexagonal dynamic AER benchmark problem with HEXTRAN. Proceedings of the third Symposium of AER. Piestany, Slovakia 27 September - 1 October 1993. Budapest: KFKI Atomic Energy Research Institute, 1993. Pp. 293 - 301. VI Kyrki-Rajamaki, R. & Stenius, T. Calculation of local boron dilution accidents with the HEXTRAN code. Proceedings of the International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses. Portland, OR 30 April - 4 May 1995. La Grange Park, IL: American Nuclear Society, 1995. Pp. 274 - 283. VII Gacs, A., Kereszturi, A., Telbisz, M., Siltanen, P. & Kyrki-Rajamaki, R. New safety analyses of RIA and ATWS events for Paks NPP. Proceedings of the International ENS TOPical Meeting TOPFORM ’95, Today’s Cost Competitive NPP for Current and Future Safe Operation. Avignon 24 - 28 April 1995. Paris: Societe Frangaise d’Energie Nucleaire, 1995. Pp. 319 - 331. VIII Antila, M., Siltanen, P. & Kyrki-Rajamaki, R. Study of core response in reactivity accidents due to local dilution of boric acid concentration. ENC ’94 International Nuclear Congress - Atoms for Energy. Lyon 2 - 6 October 1994. Berne: European Nuclear Society (ENS), 1994. Transactions. Vol. II. Pp. 105 - 111.

5 The disputant has written papers I, IV and V, and served as the leading author of papers III and VI. In paper II the author ’s contribution is the description of the dynamics calculation system. In papers VII and VIII the author has developed the conservative methods for studying the core response with the HEXTRAN code, and has performed the analysis calculations with it. The disputant has created the three-dimensional kinetics model for HEXTRAN and developed the original version of HEXTRAN, which has been used in the applications reported in the publications. At present the disputant is participating in and coordinating the further development of HEXTRAN in the reactor analysis group of VTT. The disputant ’s contribution to three-dimensional reactor dynamics studies has also been reported in Refs. [1] - [11] and to one-dimensional studies in Refs. [12] - [19].

6 TABLE OF CONTENTS

ABSTRACT ...... 3

PREFACE...... 4

LIST OF PUBLICATIONS...... 5

1 INTRODUCTION ...... 8

2 REACTOR DYNAMICS CALCULATION SYSTEM...... 10 2.1 Code system for VVER reactor physics and dynamics at VTT . 11 2.2 Models of HEXTRAN...... 13 2.3 Further development of HEXTRAN ...... 17

3 TIME-DEPENDENT SOLUTION OF NODAL NEUTRONICS EQUATIONS IN HEXTRAN...... 19 3.1 Solution of nodal flux shapes ...... 20 3.2 Solution of nodal flux amplitudes ...... 24

4 VALIDATION OF HEXTRAN ...... 28 4.1 International benchmark problems ...... 28 4.2 Validation of front modelling ...... 32

5 APPLICATION OF HEXTRAN TO ACCIDENT ANALYSES ... 34 5.1 Conservative accident analyses with a best-estimate three-dimensional code ...... 34 5.2 Hot channel methodology ...... 37 5.3 Examples of HEXTRAN applications ...... 38

6 CONCLUSIONS...... 41

REFERENCES...... 42

PAPERS I - VIII

7 1 INTRODUCTION

In the core of a nuclear reactor there are many different physical phenomena continuously interacting with each other. The temperatures and densities of fuel, coolant and absorbers change the behaviour of the neutrons, which affects the number of fissions and thus the amount of energy produced. During transients and accidents of a nuclear power plant, the power of the core changes with time. In reactor dynamics this time- dependent power behaviour is studied with computer codes that include submodels for all the relevant phenomena. Already for a long time, the bumup and power distribution calculations for accurate fuel management have been made with three- dimensional codes, because this work can be carried out with static calculations. Transient and accident analyses have almost exclusively been made with codes including only point kinetics or axially one-dimensional models for neutron dynamics. The earlier attempts in the three-dimensional calculations have been considered mainly as a curiosity because of their uncertain accuracy, poor applicability and large computer time consumption. However, in recent years the capability of computers has enormously increased and now an effective use of three-dimensional models is possible also in reactor dynamics. The safety requirements of nuclear power plants have increased all the time. After the Chernobyl accident ever more complicated accident conditions have been examined where strong interactions prevail between neutron kinetics and thermal hydraulics. Therefore, reliable transient and accident analyses can be made only with three-dimensional models. There exist also such design basis accidents which cannot be properly calculated with one-dimensional models without using very conservative assumptions. The behaviour of the cooling system of a nuclear reactor affects the conditions of the core. Local neutronic or thermal hydraulic disturbances can originate from the core or from the cooling circuits. In many analyses it is necessary to calculate simultaneously both the core and circuit conditions. New, complex fuel designs are being developed and the optimization of fuel management is becoming more important. Many projects are also going on with the aim of increasing the nominal power level of nuclear reactors. In these new conditions the safety margins in transient and accident analyses can be proven acceptable only with accurate three- dimensional calculations.

8 In the following chapters the development, validation and application of a three-dimensional reactor dynamics code called HEXTRAN (HEXagonal TRANsient analysis code) is presented. In Chapter 2 the reactor dynamics calculation system of VTT for VVER-type nuclear reactors is described. HEXTRAN is developed as an integral part of the system and it is also coupled with the thermal hydraulics model SMABRE (SMA1I BREak accident analysis code) for cooling circuit modelling. The solution is derived to the time-dependent three-dimensional nodal neutronics equations of HEXTRAN in Chapter 3. Chapter 4 of the thesis describes the validation work of HEXTRAN. Finally, in Chapter 5, the methods are illustrated, how to apply an accurate best-estimate code in accident analyses, and some application examples are given. A description of the models used in HEXTRAN is also presented in paper I. The reactor physics and dynamics calculation system of VTT for VVER-type nuclear reactors is described in papers II and III. The validation of the HEXTRAN code is summarized in paper IV. As a part of validation, sensitivity studies have been carried out on the accuracy of the different models and discretization methods used in HEXTRAN. International benchmark problems have been defined and utilized for this purpose, which is described e.g. in paper V. In accident analyses of light water reactors, many complicated phenomena arise which cannot be correctly solved by the hydraulic solution methods applied so far in the world. Presently the thermal hydraulics models of the reactor dynamics codes are being further improved by using a new solution method developed at VTT. The superiority of this new algorithm in calculating the propagation of a boron dilution front through the reactor core in natural circulation conditions is demonstrated with HEXTRAN in paper VI and the degree of conservatism of the original thermal hydraulics model of HEXTRAN is estimated. A typical example of a design basis accident, which cannot easily be calculated without a three-dimensional core model, is the control rod ejection accident. An application of HEXTRAN to its analysis is presented in paper VII. Possibilities of local boron dilution have recently been found to be a potential cause for a reactivity initiated accident. Extensive studies with HEXTRAN have been made on the core response to local boron dilution under different conditions for the Finnish Loviisa nuclear power plant. The part of this work concerning power and startup conditions is summarized in paper VIII.

9 2 REACTOR DYNAMICS CALCULATION SYSTEM

In reactor dynamics analyses both the neutronics and thermal hydraulics play an important role. The neutron kinetics is modelled at least with axially one-dimensional models. The thermal hydraulics in the core has to be modelled with greater accuracy than in large thermal hydraulics system codes with neutron point kinetics models, because the steam distribution in the core is decisive to the behaviour of the neutrons. The fission power in the core is released in fuel and in coolant both promptly and as decay power. The heat is conducted in the fuel and transferred between the fuel cladding and coolant with many different mechanisms. All these physical processes and their couplings have to be modelled in a reactor dynamics code, see Fig. 1.

Power to coolant HYDRAULICS HEAT CONDUCTION IN FUEL ROD v Heat transfer mechanisms

Coolant and ' Heat flux / Surface soluble poison 'temperature properties of fuel rod/

HEAT TRANSFER* FROM CLADDING _ TO COOLANT

Power \ Doppler directly temperature to coolant Power in ^ DIFFUSION ^ fuel PARAMETERS WITH FEEDBACKS.

NEUTRONICS

Fig. 1. Coupling of physical processes in the core of a light water reactor.

In carrying out reactor dynamics calculations we need accurate data, suitable models, and good numerical solution methods. Continuous efforts have to be made in all these sectors to improve the reliability and applicability of the reactor dynamics code system.

10 2.1 CODE SYSTEM FOR VVER REACTOR PHYSICS AND DYNAMICS AT VTT

In Finland, VTT has a comprehensive calculation system for reactor physics and dynamics analyses. It consists of code systems for both types of the Finnish plants: VVER and BWR nuclear reactors, Fig. 2. All the reactor dynamics codes have been developed at VTT. Many indigenous computer codes had to be developed because Finland was the only country outside the former CMEA countries using VVER-type reactors, which in many respects differ from other pressurized water reactors (e.g. hexagonal fuel assemblies and horizontal steam generators). With the VVER-modelling experience, models were developed also for BWRs. Well-known and widely used reactor physics codes have been acquired through data banks (e.g. OECD/NEA and RSIC) to supplement VTT’s code system. As compensation, some Finnish codes have been delivered to the data banks. The recent development of the code system for VVERs is briefly described in paper II. The first step in the reactor physics and dynamics code system is that the basic nuclear data as a function of energy are compiled into evaluated data libraries. Program-specific cross-section libraries are generated from these data bases with special processing codes. The program-specific libraries typically have a 25 - 100 energy group structure for use in the spectral codes. At VTT, a hexagonal adaptation, CASMO-HEX, see paper II and Ref. [20], has been developed on the basis of an early version of the Swedish spectral code CASMO [21] for calculation of bumup-dependent two-group constants for fuel assemblies. The next step is the three-dimensional static bumup simulation code which calculates the reactivities and power and burnup distributions in the whole core. HEXBU-3D [22, 23, 24] was originally developed at VTT for the fuel management of Loviisa as early as the seventies. On the basis of HEXBU-3D, a three-dimensional reactor dynamics code HEXTRAN has been developed, paper I and Refs. [1, 2, 3], The fuel heat transfer and parallel channel thermal hydraulics models of HEXTRAN are based on the models of the one-dimensional reactor dynamics codes of VTT. Fig. 3 shows the HEXTRAN development as a part of the reactor dynamics calculation system of VTT. VTT has long experience in the development and application of one­ dimensional reactor dynamics codes. TRAWA [25, 26] is the early light water reactor core model. TRAB [27, 28] includes, besides the core model, also the full boiling water reactor circuit models. SMATRA [29] is a code for VVERs where the TRAB core model and the SMABRE thermal hydraulics circuit model [30, 31] are coupled.

11 Basic nuclear data ENDF/B, JEF

Nuclear data processing NJOY

Nuclear data libraries CASMO libraries (25 - 70 energygroups)

Calculation of CASMO assemblywise two- i CASMO-HEX group constants rectangular L hexagonal

Calculation of reactivities, BOREAS HEXBU-3D power and bumup distributions etc. BWR VVER

Data transfer and condensation for one­ CROCO dimensional group constants

One-dimensional dynamics TRAB SMATRA codes BWR PWR

Three-dimensional TRAB-3D HEXTRAN dynamics codes BWR VVER ____ J

C P = codes developed by V'lT C:’... ' ■> = codes partly developed by VTT CZD = codes applied by VTT

Fig. 2. VTT’s calculation system for reactor physics and dynamics. 1-Dim. Core TRAB TRAB- SMATRA CORE

Full BWR Model Dyn. Full VVER Model SMABRE Stat. Neutr.

HEXBU-3D HEXTRAN HEXTRAN- WER Circuit SMABRE 3-Dim. Core

Fig. 3. HEXTRAN development as a part of the reactor dynamics calculation system of VTT.

SMATRA has been applied extensively in updating the Loviisa final safety analysis report, [15, 16], as well as in the analysis of anticipated transients without scram (ATWS) for which it was originally planned. In addition to Loviisa, ATWS analyses have also been made for the Hungarian Paks nuclear power plant, and for the new Russian VVER-91 concept, see Refs. [17, 18], and papers 111 and VII. However, after completing HEXTRAN and coupling it with the circuit model SMABRE, all analyses at VTT have been made with the three-dimensional code. Mainly two reasons can be seen for this: firstly, the analyses are easy and accurate in any conditions due to the inherent consistency between the fuel management code HEXBU-3D and HEXTRAN, and secondly, with modem computers the calculations of even the longest accidents studied in the safety analyses are feasible with an effective three-dimensional code.

2.2 MODELS OF HEXTRAN

In the following section, a brief description is given of the models of the original version of HEXTRAN used so far in the applications. More details of the code structure can be found in paper I and in Refs. [1, 2, 3]. The fuel heat transfer and coolant thermal hydraulics models are presented in detail in the TRAB manuals [25, 26, 27]. The full presentation of the nodal expansion method of HEXBU-3D used also in HEXTRAN neutronics is found in Refs. [22, 23, 24]. In Chapter 3 the derivation of the kinetics

13 equations of HEXTRAN is carried out. The neutron kinetics model of HEXTRAN solves the two-group diffusion equations in homogenized fuel assembly geometry with a sophisticated nodal method. Within nodes the time-dependent two-group fluxes are represented by linear combinations of two time-dependent spatial modes, the fundamental and the transient mode of solution. The dynamic equations include six groups of delayed neutrons. The feedback effects from xenon and samarium poisoning, fuel temperature, moderator density and temperature, and soluble boron density are included in the program. A detailed description is included for the moving fuel assemblies of big follower-type control elements which are used in the VVER-440-type reactors [23], and the effects of moving fuel temperatures, decay power and delayed neutron precursors are described even during fast transients [1], In excess of full core calculations, calculations utilizing core symmetries of half-core, 1/3 or 1/6 core can be carried out. Thermal hydraulics in the core is calculated in separated axial hydraulic channels, which connect freely with one or several fuel assemblies. Core bypass channel and unheated channel parts below and above the core can be included in the model. In VVER-440-type reactors there is almost no mixing between the hydraulic channels in the core because there are shroud tubes around individual fuel assemblies. Channel hydraulics is governed by the conservation equations for steam mass, water mass, total enthalpy, and total momentum, and by appropriate correlations [25]. The mass flow distribution between the channels is determined by the pressure balance over the core. The phase velocities may be interconnected by an algebraic slip, e.g., the drift-flux formalism. The properties of water and steam are represented as rational functions of pressure and enthalpy. Both universal or plant-specific hydraulic correlations are included in the code and they can be chosen by the user. In order to get an accurate representation of the fuel temperature- dependent Doppler feedback, the heat transfer calculation with several radial mesh points is always made in each fuel assembly for an average fuel rod. The release of prompt and delayed nuclear heat in fuel and in coolant is modelled [27]. The heat conduction equation is solved according to Fourier’s law with temperature-dependent thermal properties of fuel pellet, gas gap and fuel cladding and with different heat transfer coefficients for different hydraulic regimes [25, 26]. Advanced time integration methods are used. Time discretization is made by implicit methods which allow flexible choices of time steps. The numerical method can be varied between the standard fully implicit theta method and the central-difference theta method in fuel and cladding heat transfer and thermal hydraulics conservation equations [25]. In Fig. 4 the calculation procedure in HEXTRAN is shown for a time

14 PROCEDURE FOR A TIME STEP IN HEXTRAN

- Disturbances - Delayed neutron and time discretization source calculations - Delayed power calculation - Prediction of new fission power and flux levels

OUTER ITERATION

PRESSURE BALANCE ITERATION

- Heat transfer in fuel connected to a channel - Hydraulics

CONVERGENCE OF HYDRAULICS

- Diffusion parameters of nodes with feedback effects - Coupling coefficients between nodes on the basis of node inside flux distributions

INNER ITERATION OF NEUTRONICS

- Assembly wise flux levels

CONVERGENCE OF FLUX LEVELS

CONVERGENCE OF NEUTRONICS AND HYDRAULICS

- SMABRE thermal hydraulics - Conditions of hot channels into a file for TRAB

Fig. 4. Calculation procedure in HEXTRAN during a time step.

15 step. The neutronics and thermal hydraulics are strongly coupled in the reactor core and mutual iterations are needed to achieve a stable solution. The solution method of SMABRE is non-iterative and there is a loose coupling between it and HEXTRAN, therefore no iterations are made with the circuit hydraulics. The power distributions and boundary conditions of the thermal hydraulics of one or several fuel assemblies can be saved in a file at each time step in order to make hot channel analyses afterwards with the TRAB code. Additional hot channel factors, different fuel and channel properties, or different correlations can be applied in these, very fast, calculations in order to make comprehensive sensitivity studies. Besides the three-dimensional neutronics model, HEXTRAN includes the rather versatile fuel pellet heat transfer model. The effects of different fuel properties can be studied in real intricate accident conditions. The consequences of the deterioration of the fuel pellet properties with increasing bumup are analyzed in Ref. [11] with HEXTRAN in different reactivity initiated accidents. The circuit thermal hydraulics solution of SMABRE consists of five conservation equations for mass and enthalpy of vapour and liquid and for the momentum of the mixture. The phase separation modelling is based on the drift-flux approach. The process description is based on generalized nodes, junctions connecting nodes and heat structures describing structure walls, fuel rods and steam generator tubes. Advanced, fast, non-iterative numerical schemes applying sparse matrix solvers are used for the solution of the discretized conservation equations. The coupled code HEXTRAN-SMABRE has its own main program and some connecting subprograms, but as a rule the subprograms of HEXTRAN and SMABRE are used in the same way as in the separate codes. Both codes use their own input, output, restart and plotting capabilities. Thereby the versatility of the codes is not lost and all revisions made in the codes separately can directly be included in the coupled code. There are many projects presently underway in the world to couple the three-dimensional core models with large system codes, see e.g. Refs. [32, 33]. The coupling of a three-dimensional reactor dynamics code with a fast running system code has been found to be an effective solution also elsewhere [34]. While the first applications of HEXTRAN-SMABRE were carried out as early as in 1991 - 1992, several successive calculations between uncoupled codes were still used abroad for accident analyses demanding modelling of both three-dimensional core and full cooling circuits [35].

16 2.3 FURTHER DEVELOPMENT OF HEXTRAN

HEXTRAN is being developed as an integral part of the whole reactor physics and dynamics calculation system and all the development work of the system is also adapted to it. The latest improvements of the neutronics model are the modification of the description of the two-group constants [36] and the inclusion of the flux discontinuity factors to the nodal model [37] . The feedback description can now be given separately for all cross- sections and parabolic dependencies can be used for them. The two-group constant data is tabulated according to bumup and mean density history of moderator. On the basis of the experience of the HEXTRAN development, three- dimensional modelling of the neutron kinetics in rectangular geometry also is now carried out in order to model BWR and RBMK-type reactors. The time discretization method of HEXTRAN does not depend on nodal geometry and it can be applied as such in rectangular geometry. The new code will be called TRAB-3D (see Fig. 5). Recently, work on the RBMK- type reactors has also started again at VTT. The author performed the first RBMK calculations at VTT with the TRAB code on the possible causes of the Chernobyl reactivity accident [19]. These calculations were continued by further one-dimensional dynamics analyses [38] and by reactor physics studies with the CASMO-HEX code [39].

BWR (RBMK) WER

TRAB HEXTRAN HEXTRAN- SMABRE

TRAB- TRAB-3D HEXTRAN- HEXTRAN- PLIM PLIM PLIM CIRCUIT

Fig. 5. Further development of HEXTRAN and TRAB.

17 In light water reactor accident analyses, many complicated phenomena arise which cannot be correctly solved by the hydraulic solution methods so far applied in the world. In order to be able to analyze increasingly complex accidents outside the original applicability range of the codes, the thermal hydraulics models of the reactor dynamics codes are being further developed. PLIM, Piecewise Linear Interpolation Method, is a new highly accurate shape-preserving characteristics method for solving systems of one ­ dimensional hyperbolic partial differential equations [40, 41]. PLIM is applicable and accurate when conventional methods are accurate and it is able to treat propagating distributions of piecewise linear shape accurately on a mesh grid. In a one-dimensional time-dependent case, interpolation with the piecewise linear polynomial approximation containing two unknown parameters yields the desired shape-preserving scheme. The conservation laws are not violated either. The PLIM method has been successfully tested in several demanding flow problems, e.g. stratified two-phase flow, gas dynamics and various convection diffusion problems [42, 43]. The numerical solution can handle all types of reversed flow. Strong interactions due to source terms of the flow equations are allowed and movable discontinuities such as water levels can appear or disappear. The new hydraulics solution method has been included in the core channel models of HEXTRAN in the same way as in TRAB, Refs. [44, 45, 46], and the first test and validation calculations have been made, described in paper VI. In future, the whole of the cooling circuits will be modelled by the PLIM solution method in HEXTRAN.

18 3 TIME-DEPENDENT SOLUTION OF NODAL NEUTRONICS EQUATIONS IN HEXTRAN

The three-dimensional reactor dynamics code HEXTRAN is based on the three-dimensional static core simulator code HEXBU-3D and on the axially one-dimensional reactor dynamics code TRAB. In developing HEXTRAN one of the aims was to utilize the subroutines of the existing validated codes as much as possible. Therefore, solutions with similar forms to those used in HEXBU-3D and TRAB were sought for the equations of HEXTRAN. However, the application of the ready codes was far from trivial. One can see this from the number of variables needed for a node in dynamic calculations being much larger than in static calculations. In the original version of HEXTRAN, 115 node variables were needed for neutronics and heat transfer modelling, compared with 53 in HEXBU-3D, which also includes the bumup calculation variables omitted in HEXTRAN. The above number does not yet include the variables for hydraulic channels. Because of the complexity of the time-dependent hydraulics, common channels can be determined for several fuel assemblies in HEXTRAN if computational space or time is wished to be spared. In HEXBU-3D and HEXTRAN, a two-level iteration technique is applied in the solution of the two-group flux and power distributions. In inner iterations the average flux values over nodes are calculated; the global flux distribution of the core is adjusted with one unknown per node and the information of the internal flux shapes within the nodes is contained in the nodal coupling coefficients during inner iterations. The internal flux shapes within the nodes, and hence the coupling coefficients based on the nodal flux shapes, are improved in outer iterations. The diffusion parameters are also recalculated during outer iterations in order to take into consideration the reactivity feedback effects of the new flux and power distributions. This type of two-level iteration has proven to be very fast, only a few time- consuming outer iterations are needed in the calculations of the power distribution. Thus it is particularly suitable for a dynamics code because a dynamic analysis can include thousands of power distribution calculations. In HEXTRAN the time discretization of neutron kinetics equations for nodal flux amplitudes is made with the same advanced implicit time integration method which is also used in TRAB [25]. The resulting equations are derived in section 3.2 and they are of the same form as in a stationary source problem. The calculation of this global flux distribution includes the most important part of the time-dependency. It takes place in the inner iterations of neutronics where the application of a source problem is straightforward. However, in the outer iterations, where the coupling coefficients between the nodes are recalculated, different approximation for the time dependencies must be found in order to maintain the HEXBU-type solution model [22]. A new approximation, described in the following section, is

19 applied in the time-dependent solution for the nodal flux shapes. In the - stationary state the HEXTRAN solution is inherently consistent with the HEXBU-3D solution, i.e. the neutronics equations are the same.

3.1 SOLUTION OF NODAL FLUX SHAPES

The basic time-dependent two-group equations solved in HEXTRAN are within each homogenized node of the form

1 + [Ea/(0+S12(01 4>fijt) Vj(0 dt (1) [1-PI Sfi,t) +

1 d$ 2 (r,t) D2(r)V2<|)2(r,r) + Sa2(r)i(^0 (2) v2 (t) dt where subscripts 1 and 2 refer to the fast and thermal groups, respectively, and t = time 7 = spatial coordinate inside a node

The fission neutron source is of the form S/r,t) = (vEy )i(#,(r,f) + (vZf)2(t)

In the following, the time dependencies of the above equations will not be written explicitly. At a certain time r; all diffusion parameters in the equations are homogenized piece-wise constants inside a node.

20 Two assumptions are made inside a node. The assumptions do not have much effect on the internal flux distributions. Assumption 1: d4>j(r) at time tx (4) dt where i = 1 or 2 for fast and thermal group, respectively and (X; = constant at time t}.

(X; is determined as

71 70 4>,- ~ 4>, (5) At where ({)/ and are node average flux values at times t, and t0 = t, - At. Assumption 1 means that the flux distribution inside a node and at a time interval is assumed to be separated in respect of the time variable and the spatial variable. Approximations of the same kind are used in the three- dimensional nodal reactor dynamics codes ARROTTA [47] and DYN3D [48] and will also be used in a new code which is being developed on the basis of the static code PRESTO II [49]. Assumption 2:

SAr ) = ~ SAr) at time t (6 )

where Sd and Sf are node average values. Assumption 2 means that the delayed neutron source at a time has inside a node the same distribution as the prompt fission neutron source. Effectively the same approximation is made in all three-dimensional reactor dynamics codes, see e g. Refs. [47, 48, 50, 51], because otherwise the flux distributions inside the nodes and the precursor amplitudes at each node should be saved at each time during the whole dynamics calculation and a huge amount of computer memory would be used to an insignificant end. Hence, the advantage of the use of the accurate nodal method would be lost. With these two assumptions Eq. (1) becomes

Sa/+S12 + “lVl1 " f l) 4>i(r) , S/y (7)

+ d; i-p+^ (v 2/ )2

21 and Eq. (2) -i - D S«2 + a 2V2 D2 Si2l(r) = 0 (8)

The errors due to Assumptions 1 and 2 do not have much effect on the flux distributions inside the nodes because a, v-1 is small compared to Za, Sd / Sf is small compared to l. The errors are comparable to those caused by bumup in the static calculations. Usually the assemblies are radially described with one homogenized node, but the bumup inside the assembly can change significantly due to different flux levels between the fuel rods. Still the static calculations have been shown to be accurate enough. However, generally it is known in reactor physics that also small systematic errors may cause substantial flux tilt. For this reason, the comparison of calculations with measurements is of great importance. In HEXTRAN the analytical theory of HEXBU-3D [22, 23] is used to solve the coupled set of diffusion equations with constant coefficients at a time, Eqs. (7) and (8). In the following, this theory is briefly outlined in order to make the solution principle understandable. The general solution to Eqs. (7) and (8) is a linear combination of two characteristics solutions or spatial modes //r) and /7/r). The //r) is called the fundamental mode and the/j/r) is called the transient mode. The spatial shapes are determined by the Helmholz equations

(V2 * S,2)/,(r) - 0 (9)

(V2 - fl,2)/» - 0 OO)

B, and Bu are the characteristic bucklings of the modes and they can be determined by substitution of trial solutions of the form

4>,(r) =/(r)

22 D,S2 + S0, -(l-p+^HvS^, -(l-p^)(v2/)J

„ a, '12 £>„52 + 2.., + —

= 0 (12)

These equations have a nontrivial solution only if the determinant of the matrix is zero. Setting the determinant to zero we get a second-order equation for B2 . The two roots of this equation are the characteristic bucklings B2 and -B,,2 of the spatial modes. The fast and thermal fluxes are related to the spatial modes in the following way

4>,(r) = fM) + R„Mr) (13)

'12 */ = (i + gfr")-' (Sa2+a2/V2) (14) (^o2 + Rn (1 - b\uI) = 12 and where

,2 (15) (S a2 ajv?)

The fundamental mode or asymptotic mode f/r) is positive in both energy groups. The buckling B2 is relatively small and corresponds to the conventional material buckling. The fundamental mode contributes to a major part of the flux in both energy groups. In a light water reactor the buckling -B,2 is large and negative and roughly equal to -l/L2 . The transient mode /,/r) is significant only near discontinuities in material properties. It is of opposite sign in the fast and thermal groups and its relative contribution to the thermal flux is about an order of magnitude greater than to the fast flux. The spatial modes are modelled and the continuity conditions and coupling coefficients between the nodes are determined in HEXTRAN in the same way as in HEXBU-3D [23]. Their derivation is not repeated here.

23 3.2 SOLUTION OF NODAL FLUX AMPLITUDES

When Eqs. (1) and (2) are solved during inner iterations in order to get the fundamental mode amplitudes of nodes, a more accurate time discretization method is applied than in the solution of the flux distributions inside a node. Equations (1) and (2) are of the form

= E

The spectral matching method Wn developed by Devooght and Mund [52] is applied in HEXTRAN with the same choices as in TRAB. The Wn method is based on the idea that the eigenvalues exp(X EiAt) of the advancement operator exp(AtE) can be approximated by a rational function of XE,

a£,at b(At)+d(At) XE At e = ------+ truncation error (17) a(At) -c(At) XEjAt

The parameters a, b, c, and d can be determined so that the A- stability condition is satisfied and the expression in Eq. (17) is exact for some eigenvalues X.£, of E. (A-stability means that the convergence factor is less than a constant which is less than one.) The particular choice of TRAB is (with more detailed arguments given in Ref. [25]) : (3c2"1+ 1 )u, a = ------e^-1

/'(/"'+3)w, b = ------2m, 1 e -1 (18) c = 1 d = eu‘ where ux = \E{ At , X£, s 0

The above choice of the coefficients of the rational function in Eq. (17) has the same purpose as the use of the point kinetics in the quasistatic method viz. to allow to take into account the global time variation of the reactor power more precisely. With this choice it is valid that ~b<^° = c^V + S1) + d(£°0+S°) + 0(Ar2) (19) At

24 where the truncation error is of second order in At. The accuracy is of the same order as with the central-difference method. Additionally, one avoids the weakly decaying oscillations which sometimes occur in the central- difference method. On the other hand, the stability is not achieved at the expense of the accuracy as with using the standard fully implicit method. A good choice for XE, used in HEXTRAN is - I 1/T I, where T is the period determined on the basis of the total power behaviour. This choice takes very accurately into account the time variation of the total power. This is of great importance because the total power can change with a factor of 108 while the relative power distribution typically changes locally at most with a factor of about ten. When we neglect the truncation error in Eq. (19) we get - £lj 4>l = S1 + Q1 (20)

where we have collected the terms depending only on the values of the previous time step to a new source term Q1 b_ = + d E° 4)° + d S° (21) At /

When we write Eq. (20) for and use it to eliminate £° in Eq. (21) we get a recurrence formula for Q

Ql -d Q° + 4>° (22)

We do not need to know E1 and E° or to operate with them to get Q1, i.e., this source term does not change during the iterations for a time step and we do not have to preserve the cross-sections of the former time step for its calculation. The delayed neutron source in Eq. (1) is

Sd(r,t) = £ (23) j

where Xj = decay constant of delayed neutron precursor group j Cj = concentration of the j’th delayed neutron group. It follows from Assumption 2 that the distribution of the delayed neutron precursor concentration inside the nodes is at a time the same as the prompt fission neutron source distribution. In the following we omit the space variable and handle only the node average values.

25 The time-dependence of the delayed neutron precursors is given by

Cft) = p;. fe~X^tf) Sf(t) dt ' + Cft^ e 'X^~

where (3; = fraction of delayed neutron precursor group j. We can achieve the accuracy of second order in At also in the treatment of the delayed neutrons by assuming that the fission neutron source Sf varies linearly during a time step. A recurrence formula is obtained from Eq. (24)

c) = C,VX'A‘ + p.T!.(A t)Sf° + (25)

where

+ (26) kjX

and = ~4-(V1+e’V) (27) X]x

The analytically integrated expressions for r\j and ^ allow arbitrary time steps in Eq. (25). All bumup dependence of the delayed neutron parameters is taken into account in (3, and the values of Xj are kept constant. Therefore rj; and ^ are numerically calculated only once during a time step for the entire core, and the computer time consumption is of no importance. The delayed neutron source Sj can be divided into two parts, from which the first part can be considered as the known source Sd° S°d = ^(X.e'^'C^X.p.n/AOS;) (28)

and the rest is proportional to the prompt fission neutron source and can be added to it. Thus, the total coefficient of the fission neutron source in the time discretized form of Eq. (1) will be 01 = (1-P)+Z W/AO (29)

In order to get the exact coarse mesh equations for the inner iterations, Equations (1) and (2) are integrated over the nodal volume. Then the equations are summed together to get one equation on the average values of the fundamental mode fluxes. Applying Eqs. (20) and (22) to

26 discretize Eqs. (1) and (2), and using the Eqs. (3), (25), (28) and (29) for the source terms, we get

E + r* [2&+4)1 + [ZL+4.2 I Arv, Afv2* (30) = 0U Vk [(vSz)* 5? + (vSz)2 Vh + Vk [Qlk + Qlk + 5°*] where superscripts k = index of the node l = index of the neighbouring nodes and AkI = area of the interface between the nodes V* = volume of the node /-*' = current density from node k to node / and the bar over a variable means the average value over the node or interface. The current densities depend on the fundamental mode fluxes of the node and its neighbours through the coupling coefficients in the same way as in HEXBU-3D and the derivation is not repeated here. The node average values of the fast and thermal fluxes are also represented with the node average values of the fundamental mode flux. By making these substitutions we get the basic nodal equation for inner iterations, which is of the form

2] ( // ) + = 8'* (vz/// + oj* (31) i where K = coupling coefficients between the nodes Qjk = sum of the source terms in Eq. 30. The form of Eq. (31) is the same as the form of a stationary equation with source terms. The only formal difference between it and the corresponding stationary equation in HEXBU-3D is the inclusion of the source terms in the dynamics equation. However, the source terms of Eq. (31) can be treated similarly to the terms depending on the flux levels of the neighbouring nodes, and the use of the same line overrelaxation technique in HEXTRAN as in HEXBU-3D is straightforward. The whole time discretization system is implicit and no instability problems arise apart from the accuracy. The accuracy depends, of course, on the length of the time steps. The work is still being continued in the world to develop and apply stable and accurate time discretization methods for the kinetics equations. A method with similar purposes as the method in HEXTRAN has recently been published for the new one-dimensional space-time reactor kinetics model of the RELAP5 code [53].

27 4 VALIDATION OF HEXTRAN

The main validation work of HEXTRAN is summarized in paper IV. HEXTRAN is based on already validated codes and the models of these codes have been shown to function correctly also within the HEXTRAN code. The main new model of HEXTRAN, the spatial kinetics model has been successfully validated against the Czech LR-0 test reactor and Loviisa plant measurements. In stationary state HEXTRAN has been shown to give almost identical results with HEXBU-3D in various fuel cycle and power level conditions. There are small differences only due to the thermal hydraulic feedback effects because the detailing level is different in the thermal hydraulics models of the codes. HEXTRAN uses the same nuclear data as HEXBU-3D and its neutronics solution is inherently consistent with HEXBU-3D. The reactor physics data base has been thoroughly validated against detailed Loviisa measurements. The whole hexagonal reactor physics code system of VTT was also extensively validated in the TIC (Temporary International Collective) cooperation utilizing the results of its comprehensive experi ­ mental program and comparison calculations between different codes [54]. A thorough intercomparison work has been carried out between all Finnish reactor dynamics codes to ensure that compatible results are achieved in all situations. The assessment and validation of the one-dimensional reactor dynamics codes of VTT, TRAB and SMATRA, have been reported in Refs. [4, 12, 13, 14]. Friction and heat transfer parameters used in the reactor dynamics analyses of the VVER plants are studied in Ref. [55]. Accurate modelling of these properties is decisive in the hot channel analysis. The separated hot channel analysis method, which is a standard tool in the analysis of the most severe thermal hydraulic conditions in a fuel bundle, seems to be conservative at least in the forced flow conditions.

4.1 INTERNATIONAL BENCHMARK PROBLEMS

As a part of the validation work, sensitivity studies have been carried out on the accuracy of the different models and different discretization methods used in HEXTRAN. International benchmark problems have been utilized for this work in addition to their primary aim to make comparisons between the different codes. Until recent years there have been only a few realistic dynamic benchmark problems defined in the world. In 1991 the committee NEACRP of the Nuclear Energy Agency of OECD introduced benchmark problems

28 aimed at assessing the discrepancies between three-dimensional square lattice codes for transient calculations in LWR cores [56]. The benchmark problems were participated in with most of the three-dimensional rectangular dynamics codes in the world. Participation also with one ­ dimensional codes was strongly recommended and all PWR and BWR cases were successfully calculated with VTT’s axially one-dimensional TRAB [57]. The effectiveness and correctness of the time discretization methods of TRAB used also in HEXTRAN were demonstrated. On the basis of the NEACRP benchmark problems for PWRs, also a hexagonal benchmark problem has recently been defined [58]. The core thermal hydraulics models included in these PWR benchmark problems are simpler than the HEXTRAN core thermal hydraulics; no pressure balance exists over the core and the mass flow distribution over the core channels is even. The first three-dimensional hexagonal dynamic benchmark problem was defined in 1992 in AER (Atomic Energy Research for Investigating Neutron Physics and Thermohydraulics Problems of Reactor Safety), Refs. [59, 60]. It simulated a rod ejection accident in a realistic VVER-440 core. However, no feedback effects or thermal hydraulics were included in the first benchmark for two reasons: firstly, to be able to gradually clarify the reasons of the possible discrepancies of the results, and secondly, to maximize the number of possible participants because KIKO-3D [61] and BIPR-8 [62] codes did not yet have any thermal hydraulics modelled. In the second benchmark, Refs. [63, 64], the Doppler feedback effects were included in the problem but an adiabatic case was calculated in order to make a moderate increase in the complexity of the problem. The third benchmark includes the whole thermal hydraulics in the core and a hot channel model with departure from nucleate boiling and film boiling calculations, Refs. [5, 6], However, the circuit models have not yet been included in the benchmark problem definitions, so all HEXTRAN capabilities with SMABRE coupling cannot have been included in the comparisons. All hexagonal dynamic AER benchmark problems have been calculated with HEXTRAN. The other three-dimensional hexagonal dynamics codes with which there have been participants in all or some of the problems are: DYN3D from Germany [48, 65], KIKO-3D from Hungary, BIPR-8 from Russia, (as a separate kinetic code without thermal hydraulic feedback modelling or as coupled with the well-known German ATHLET code), and APROS from Finland [66]. The benchmark problems will be calculated in the future also with another code from Russia, NOSTRA [67]. NOSTRA is being developed on the basis of the static code BIPR-7 which is used for the fuel management of the Russian VVER plants. NOSTRA will include Russian thermal hydraulics models for the core and the cooling circuits.

29 The results of the two hexagonal dynamic AER benchmark problems without thermal hydraulics have shown close agreement, see Fig. 6. Also the power distribution results of HEXTRAN and the other three high-order nodal codes have been in good agreement. In the third hexagonal dynamic AER benchmark problem, more discrepancies are induced by different hydraulics modelling, particularly in the hottest channels where boiling occurs [6],

100000.0

80000.0

Mill :

60000.0

i----- DYN3D/M2 '------BIPR8: • KIK03D 40000.0 "HEXTRAN

20000.0

Time (s)

Fig. 6. Fission power versus time during a control rod ejection accident, from Ref. [64], results of the second hexagonal dynamic AER benchmark problem.

30 Fig. 7 shows the radial fission power distribution at the time of maximum power peak calculated with HEXTRAN in the third hexagonal dynamic AER benchmark problem with core thermal hydraulics included. The distribution is strongly distorted and most of the power is released near the ejected control rod. O CD o i o

5, 8000 i 60 QQ a, 40o 0

1 200q e: 0

Fig. 7. Radial fission power distribution in a control rod ejection accident.

In paper V the HEXTRAN solutions to a kinetic benchmark problem without feedback effects are analyzed (the first hexagonal dynamic AER benchmark). The two different control rod models of HEXTRAN were used in the calculations: the proper detailed description of the VVER-440-type large flux trap control rods with moving followers and the simpler cross- section model designed for the VVER-1000 finger-type control rods which have a smaller reactivity worth. The results of dynamic power behaviour were very similar calculated by both models. It was also shown that by using reasonably large time steps (0.01 s during the fast ejection and the power peak, 0.1 s afterwards) the results converged so that the shortening of the time steps did not change them. It was found that there is a good reason in accident analyses to use conservative control rod reactivity worth, higher than predicted by the best- estimate codes, because the reactivity worth is very sensitive to the nodal power distribution. If the reactivity worth is reliable, the global dynamic behaviour of the core is not sensitive to small errors in power distribution. A conclusion of the importance of the control rod reactivity worth in the control rod ejection accident was drawn also in Ref. [58] on the basis of comparisons of the results of the codes PANTHER, HEXTIME and DYN3D, but no reasons for the differences of the worths were given.

31 Axially, 10 nodes were sufficient to describe the power increase caused by a control rod ejection. However, for proper description of the locally very heterogeneous effects of reactor trip over the whole core 20 nodes were needed in axial direction. In reality, the negative feedback, not included in the benchmark, would decrease these effects. A typical number of axial nodes used in fuel management calculations is 10, but in dynamic calculations the number is too small for the thermal hydraulics modelling as well, so 20 axial nodes are usually used. Radially, one node per fuel assembly in the neutronics solution is sufficient for HEXTRAN as a nodal code. The time discretization methods used in HEXTRAN and TRAB were comprehensively studied by calculating an earlier one-dimensional benchmark problem defined by the author [14]. It was concluded that the chosen methods in different models of the code (neutronics, fuel heat transfer, flow hydraulics) must be consistent with each other. Then the calculation can be carried out without convergence problems. The results of different methods did not essentially deviate from each other, if the calculation of the whole problem could be carried out successfully without interrupting oscillations.

4.2 VALIDATION OF FRONT MODELLING

All conventional hydrodynamic models have difficulties in following the transport of sharp fronts in the coolant channels, e.g. that of a local boron dilution front. In the boron dilution analyses carried out with HEXTRAN coupled with SMABRE, the dilution slugs were simulated directly to the core inlet in order to minimize the effects of numerical diffusion, which tends to reform the boron dilution front into a ramp. However, some numerical diffusion occurs also during the propagation of the dilution front through the core, especially if the coolant velocity is low, because the neutronics calculation limits the lengthening of the time steps. If the time steps are lengthened, numerical dispersion can occur. Neither dispersion nor diffusion are of any problem for the PLIM algorithm, since propagating fronts can be handled properly within a mesh cell. Some test runs for the propagation of a sharp boron dilution front were carried out with the original HEXTRAN code and with the new code version HEXTRAN-PLIM and they are described in paper VI and Ref. [46]. In normal flow conditions, both code versions gave the same overall results, although the numerical solution of the hydrodynamic flow produced by HEXTRAN-PLIM was more accurate and close to the ideal solution. This confirms the good performance of the HEXTRAN code under normal flow conditions.

32 In natural circulation conditions the HEXTRAN-PLIM solution is again nearly exact. In HEXTRAN solution the smoothening of the edges of the boron dilution slug reduces the amplitude of the slug in the upper part of the core. The most serious consequence of the smoothening is that the reactivity worth of the boron dilution slug decreases and the fission power peak is clearly smaller than the peak produced by HEXTRAN-PLIM. In earlier analyses carried out with HEXTRAN in natural circulation conditions, the prominent effect of numerical errors on the simulation of finite boron dilution slugs has been taken into account by using conservative assumptions but too much conservatism may have been introduced into the analyses. It should be noticed that the numerical errors also affect the transport of the voids in the coolant and the enthalpy of the coolant, although these errors are harder to detect The implementation of the PLIM method to HEXTRAN guarantees that conservative accident analyses of local boron dilutions can be made even in numerically difficult flow conditions [7]. In reality some mixing occurs in the propagating boron dilution front especially in large open parts of the circuit. Hydraulics measurements on boron dilution front propagation are either underway or at the planning phase in many countries, e.g. Refs. [68, 69]. These effects can be included in the PLIM model when best- estimate calculations are needed. However, inside the reactor core mixing effects are small.

33 5 APPLICATION OF HEXTRAN TO ACCIDENT ANALYSES

The licensing analyses for a nuclear reactor must be conservative, in the sense that the phenomena affecting the analyzed accident are exaggerated, and hence the safety margin of the analyzed case can be confirmed. The conservatism is needed because of limited knowledge but also because of the need to cover a great number of similar cases with one analysis, the bounding analysis. In nuclear power plants, thousands of parameters can affect the results of an analysis. Probabilistic methods have been tried in order to take account of the uncertainty in best-estimate transient results; an application with one-dimensional RETRAN-02 calculations is in Ref. [70]. However, only the variation of a few parameters can be handled without the number of analysis calculations becoming too large. In practice, good engineering judgement is the most important asset. In three-dimensional analyses the situation is even more complicated. There is not very much experience in the world in carrying out conservative accident analyses with a best-estimate three-dimensional reactor dynamics code. The analyses reported are mostly made as best- estimate calculations, e.g. with DYN3D in Refs. [65, 71] or with RAMONA-3D in Ref. [72], where only the initial circumstances are chosen conservatively but the calculational parameters are not varied. Detailed instructions can only be given for distinct individual accident types. For instance, a control rod ejection accident methodology has been defined for the users of code ARROTTA by EPRI [73] but no easy way is given to modify the conservatisms of different parameters in the code input. In analyses of longer and more complicated accidents, e.g. ATWS, varying of key parameters can even change the nature of the accident. Possibilities to modify the neutronics parameters have been added to HEXTRAN by the author so that the conservatism of the calculations can be simply and reliably varied without changing the vast ordinary neutronics data. Also a new multiple hot channel methodology has been developed for this purpose.

5.1 CONSERVATIVE ACCIDENT ANALYSES WITH A BEST- ESTIMATE THREE-DIMENSIONAL CODE

Many neutronics parameters can or must be modified when conservative accident analyses are made with a three-dimensional best- estimate code. The most important of them are: - reactivity feedback coefficients

34 - efficiency of control rods - fraction of delayed neutrons - fraction of decay power - power distributions. Different criteria are applied in the transient and accident analyses when the acceptability of the plant response to a disturbance is studied. For instance, maximum values of primary pressure, fuel enthalpy or cladding oxidation are limited. All these parameters do not always reach maximum values with the same combination of conservative modifications. When using a three-dimensional core model the definition of conservatism is also not clear because modifications of different parameters cannot be made separately but they influence each other. A change of one parameter to conservative direction can decrease the supposed conservatism of some earlier change of another parameter. In the following some remarks are made on which are the most common modifications used in the conservative HEXTRAN analyses. The possible effects of all these modifications on the eigenvalue in steady state are compensated for by uniformly changing the fission neutron production cross-sections, which corresponds to the change in average bumup. Reactivity feedback coefficients In all reactor dynamics analyses the conservatism of different modifications can change in different phases of the transient. It might be desirable to maximize the power level. During a power increase it is then conservative to decrease the absolute value of the reactivity coefficients of the negative feedback effects. However, during a power decrease, their values should be increased. Each transient must therefore be analyzed by performing sensitivity studies in order to know which phase of the transient is most critical. In HEXTRAN the conservative values of fuel temperature reactivity coefficients are obtained by uniformly adding to the fission neutron production cross-sections small linear contributions depending on the square root of the fuel temperature of each node. The moderator temperature reactivity coefficient is changed in the same way depending on the moderator density of each node. The reactivity coefficients will change according to the applied neutronics model when the conditions in the core change. A more conservative value for the moderator reactivity feedback coefficient can also be achieved in a natural way by somewhat changing the boric acid concentrations from the critical value. Efficiency of control rods In principle the efficiency of control rods is modified for two reasons: the reactivity worth of them is not known exactly, or the analyses made in

35 certain loading conditions are desired to represent more generally also other loadings where the reactivity worth of control rods can be slightly different. The modification can be made by changing the two-group constants or boundary properties which specify the control rods. The reactivity worth of control rods is a key parameter in many types of analyses. Maximizing its value maximizes the power increase in different types of control rod withdrawal or ejection accidents. However, even the reactivity worth cannot be changed straightforwardly in the sense of conservatism: when maximizing the efficiency of the control rods also the effectiveness of the trip control rods is maximized and the core becomes more subcritical after the trip. In addition, a more effective control rod reduces the flux and power in its surroundings. Thereby the thermal hydraulics conditions in the initial stationary state are milder near the control rod, where the consequences of the control rod movement are strongest. Usually the trip efficiency is minimized by assuming a control rod to be stuck in the upper position. The position of the stuck rod is chosen according to the maximum decrease of the trip reactivity worth or by choosing a control rod situated in the most critical area during each accident. Maximizing the initial insertion of the control rods is a natural way to make conservative calculations. Fraction of delayed neutrons The fraction of delayed neutrons is one of the decisive parameters which change during the fuel cycle. It is larger at the beginning of the cycle than at the end, and it typically has an effect on the time at which the analyses of some accidents are most critical during the fuel cycle. The uncertainty of its value is often compensated for by using a somewhat decreased value, when analyzing fast power bursts. Fraction of decay power The conservatism of maximized fraction of the decay power is clear in the analyses of loss of coolant type accidents. On the contrary, in reactivity initiated accidents it is conservative to assume a minimized fraction of decay power so that the prompt power peak is maximized. However, if transients beginning with power increase are calculated as ATWS, where the power decrease is not induced by the trip, the situation is no more clear. Then the different acceptability criteria may demand different directions for the conservative changes of the decay power fractions. Power distributions In HEXTRAN analyses, the best-estimate radial power distribution is usually not changed but the axial power distribution is often modified. The behaviour of the hottest fuel rod and the hottest flow channel are usually

36 analyzed in separate calculations with TRAB based on HEXTRAN results. The conservatism for the assembly peaking factor can be included in the fuel rod peaking factor as an extra multiplier. The engineering (safety) factor is usually also included as a multiplier. The given axial power distribution of a fuel assembly is multiplied with this combined hot channel factor. In the hot channel analyses the axial power distribution cannot usually have its best-estimate form because the maximum local linear power is often given as a limiting value. However, already the experience from the analyses made with the one-dimensional dynamics code SMATRA [18] has shown that the results can be seriously distorted if the axial power distri­ bution is changed only in the hot channel analyses. The neutronics is not calculated in the separate hot channel analyses. In the case where the axial distribution is changed only in the hot channel, the strong axial reactivity feedback effects of coolant have been affecting a very different axial distri­ bution. Therefore, if it is necessary to change the initial axial power distri­ bution, it should be modified already in the HEXTRAN calculation itself by changing the mutual reactivities of the nodes at different radial levels. With the modification of the axial power distribution the maximum local linear power of the fuel rod can be changed. The modification also affects the reactivity worth of the control rods inserted partially into the core. In addition it affects the tendency to achieve the departure from nucleate boiling conditions, which most probably occurs in the upper part of the core with larger void fraction.

5.2 HOT CHANNEL METHODOLOGY

When using point kinetics or axially one-dimensional calculations there is only one possibility to calculate the hot channel. In three- dimensional analyses, there are as many different possibilities for hot channel calculations as there are fuel assemblies, but the practical work to make the calculations and to handle their results brings restrictions. If only one very conservative hot channel represents the whole core, the benefit of the three-dimensional calculation is lost. If the hot channel analyses are included directly in the three- dimensional analysis, very large computer capability is needed. There are also difficulties to parametrically handle conservatisms of the hot channels and every different loading must be analyzed individually. In HEXTRAN analyses, a new multiple hot channel methodology is used, which is in each calculated case based on the analysis of the power behaviour in different parts of the core. As far as the author knows, this kind of method has not been published elsewhere.

37 The main steps of the methodology are: - The hot channel analyses are made separately using data files containing axial power distributions and pressure differences over the core. - The core assemblies are grouped together according to time histories of assemblies during the transient. - Every group is represented by one hot channel. - Hot channel factors in every group have their maximum credible values. - The results of a typical loading can be used for all similar cycles. - Applying of conservatisms is easy. The departure from nucleate boiling or oxidation behaviour of the hot channels in other assemblies of a group are studied by repeating the calculation of the representative hot channel with different multipliers of the fission power. Comprehensive sensitivity studies can easily be done with different fuel and channel properties or different correlations in order to check the conservatism of the results. These hot channel calculations are very fast with the one-dimensional TRAB code, where the extreme phenomena modelled are the fuel temperature rise after occurrence of the departure from nucleate boiling, oxidation of the cladding material and rewetting of the fuel.

5.3 EXAMPLES OF HEXTRAN APPLICATIONS

HEXTRAN coupled with SMABRE has been extensively used in contract research both on design basis accidents and on new more exotic areas of, e.g., boron dilution and ATWS accidents. HEXTRAN-SMABRE is very effective and also such long transients as ATWS have been calculated with it; even whole core geometry has been used which allows arbitrary asymmetry in the core, e.g., due to different boron injections to different loops. In more complicated ATWS cases there can be radial asymmetry already in the original disturbance causing the accident. In recent years, HEXTRAN and the whole VVER calculation system of VTT has been increasingly utilized also for improving the safety of the VVERs in Eastern Europe. A typical example of a design basis accident which cannot easily be calculated without a three-dimensional core model is the control rod ejection accident, where considerable deformation of the radial and axial power distributions occur in the core. An application of HEXTRAN for the analysis of control rod ejection accidents is presented in paper VII. The main phenomena during a control rod ejection accident (fission power peak,

38 time of trip signals, fuel temperature increase, extent of departure from nucleate boiling occurrence) could be analyzed without modelling the cooling circuits. The accident is so fast that the core mass flow does not markedly change during the critical phase of the accident. However, the simultaneous prediction of the pressure increase can only be made with the full cooling circuit models included in the calculation. Steam line break is another type of design basis accident where significant radial deformation of fission power occurs in the core. Here the disturbance originates from the cooling circuits and this type of accident cannot be analyzed without modelling both the core and the circuits together. During the possible recriticality phase due to the large overcooling of the core after the trip, the assumption of a control rod stuck in the upper position can further distort the fission power distribution (see Fig. 8). Although the total power level would not increase to the nominal level, the conditions in the hottest part of the core must be carefully analyzed with the three-dimensional dynamics calculation and with additional hot channel calculations, because fuel overheating could occur due to departure from nucleate boiling. A three-dimensional model is also much more reliable in predicting the reactivity level after the trip. HEXTRAN has been applied in steam line break analyses for different plants.

Fig. 8. Radial fission power distribution during recriticality phase in a steam line break accident. One control rod is assumed to be stuck in the upper position.

39 Possibilities of local boron dilution have recently been found out to be a potential cause for a reactivity initiated accident in pressurized water reactors, Refs. [74, 75, 76, 77, 78]. The effects and mechanisms of local boron dilution both in normal and in standby conditions and during accidents are presently being studied for Loviisa plant and some countermeasures have been taken, Refs. [79, 8, 9, 10]. Analyses are being made to study the mixing of the local boron dilution slugs as well as to predict the conditions when an inherent boron dilution could appear during the accidents. Extensive studies have been made with HEXTRAN on the core response in reactivity accidents due to local boron dilution in different conditions. The analyses for Loviisa plant made in power and startup conditions are summarized in paper VIII. Analyses of core response to local boron dilution with very extreme requirements for the code have been carried out by the author, e.g. Refs. [8, 9, 10]. They were made in prompt recriticality conditions during shutdown, and violent boiling occurred in the core channels. The coolant velocity was varied from nominal flow to natural circulation rate. The prediction of the reactivity level during these transients was demanding even for an accurate three-dimensional code, when the conditions during one analysis calculation change from cold shutdown to the limits of fuel melting. During boron dilution accidents, two main phenomena affecting the reactivity of the core occur in the axial direction: the propagation of the dilution front and the boiling of the coolant. The consequences of the asymmetric boron dilution in the core were previously studied using the axially one-dimensional code SMATRA with the synthesis model in the radial direction [15]. These results were later compared and validated with the HEXTRAN calculations reported in paper IV.

40 6 CONCLUSIONS

The thesis describes the author ’s work on developing, validating and applying the three-dimensional reactor dynamics code HEXTRAN. The three-dimensional reactor dynamics presupposes full knowledge of both three-dimensional static reactor physics and reactor dynamics including thermal hydraulics. All HEXTRAN models are as accurate as the models in the codes developed at VTT earlier for more limited purposes, no approximations have been made to compensate for the additional complexity. Therefore, HEXTRAN must have been able to cope with all the validation cases completed earlier with the reactor physics and dynamics codes. The new mathematical solution of the three-dimensional kinetics in HEXTRAN has been developed such that the same form of equations can be used as in the older VTT codes, the three-dimensional static reactor physics code HEXBU-3D and the one-dimensional reactor dynamics code TRAB. As a result, HEXTRAN includes all the experience on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics analyses. The dynamic coupling of HEXTRAN with the thermal hydraulic system code SMABRE also allows the VVER circuit modelling experience to be included in the analyses. With HEXTRAN it is possible to perform fully realistic time-dependent analyses starting from the actual core cycle conditions of the nuclear power plant. Methods for making conservative accident analyses with this best- estimate code have also been developed. Complicated transients and accidents in which there are strong interactions between neutron kinetics and thermal hydraulics can be reliably analyzed. The new hydraulics solution method PLIM developed at VTT has been applied in HEXTRAN to remove modelling restrictions and to eliminate numerical diffusion and dispersion. The PLIM method has been shown to improve the accuracy and expand the applicability range of HEXTRAN. HEXTRAN has been validated against different types of relevant information available, viz. measurements of a test reactor, start-up experiment and other data of a real plant, as well as with the calculation of several international benchmark problems and independent code comparisons. HEXTRAN’s applicability to calculate VVER-440 and VVER- 1000-type reactors has been shown. Extensive analyses have been carried out with HEXTRAN on both design basis and new types of accidents, e.g., ATWS or local boron dilutions. The usefulness of the three-dimensionality of HEXTRAN is shown particularly in accidents with asymmetric fission power distribution originating from local neutronic or thermal hydraulic disturbances in the core or cooling circuits.

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51 Reprinted with permission from the publisher. PAPER I In: Proceedings of the first Symposium of AER. Rez near Prague 23 - 28 September 1991. Budapest: KFKI Atomic Energy Research Institute. 1991. Pp. 474 - 481.

HEXTRAN : VVER REACTOR DYNAMICS CODE FOR THREE-DIMENSIONAL TRANSIENTS

R. Kyrki-Rajamaki Technical Research Centre of Finland Nuclear Engineering Laboratory P.0. Box 208, SF-02151 Espoo, Finland Tel +358 0 456 5015, Fax +358 0 456 5000

ABSTRACT

HEXTRAN is a new three-dimensional reactor dynamics program for coupled neutron kinetics and thermohydraulics calculation of WER type pressurized water reactors. Main applications of HEXTRAN are the calculation of asymmetric accidents in core, e.g. control rod ejection, main steam line break or startup of inoperable loop, and the stability analysis in connection with Anticipated Transients Without Scram (ATWS). HEXTRAN is based on the three-dimensional stationary nodal simulator program HEXBU-3D and on the one-dimensional dynamics program TRAB which have also been developed at Technical Research Centre of Finland.

Core symmetries for full core, 1/2, 1/3 or 1/6 can be used in the calculations. A special treatment has been developed for the dynamic calculation of the moving fuel assemblies of big follower-type control elements of WER-440s. The thermohydraulics is calculated in separate axial hydraulic channels, each of which relates freely to one or several fuel assemblies. The circuit accident analysis program SMABRE has now been dynamically connected to HEXTRAN in the same way as in the program SMATRA of VTT. Different connection geometries between HEXTRAN and SMABRE can be defined.

Different reactivity initiated accidents (RIA) have been calculated (uncontrolled withdrawing of control rod group, ejection of control rods, unintended dilution of soluble boron at the core inlet). Their results have been compared with results of TRAB, which has been used for Loviisa FSAR calculations.

BACKGROUND

HEXTRAN /!/ is a new three-dimensional reactor dynamics program for coupled neutron kinetics and thermohydraulics calculation of WER type pressurized water reactor cores. Main applications of HEXTRAN are the calculation of asymmetric accidents in core, e.g. control rod ejection, main steam line break or startup of inoperable loop, and the stability analysis in connection with Anticipated Transients Without Scram (ATWS). Stability can cause problems with ATWS because there is boiling in the core due to high fission power during the period with natural circulation and in PWRs there are no stabilizing flow throttles at core inlet. HEXTRAN is based on the three-dimensional stationary nodal simulator program HEXBU-3D /2/ and on the one-dimensional dynamic neutronics and thermal-hydraulics program TRAB /3,4/ which have also been developed at the Technical Research Centre of Finland.

HEXBU-3D is used in fuel management calculations for the WER-440 type Loviisa Nuclear Power Station in Finland and it has been validated against Loviisa measurements.

TRAB has been extensively used for accident analyses of TVO ABB Atom type BWRs and Loviisa PWRs eg in connection with the revision work of Loviisa Final Safety Analysis Report /5,6/. The accuracy of the model has been validated in several ways 11/.

MODELS

HEXTRAN is designed for a reactor core that consists of hexagonal fuel assemblies which are represented by hexagonal prisms divided axially to an equal number of horizontal layers. The program solves the two-group diffusion equations in homogenized fuel assembly geometry by a sophisticated nodal method. The eigenvalue in the steady state can be either the effective multiplication factor or the boron concentration of the moderator. The dynamic equations include six groups of delayed neutrons. The feedback effects from xenon-poisoning, fuel temperature, moderator density and soluble boron density are included in the program.

A special treatment has been developed for the dynamic calculation of the moving fuel assemblies of big follower-type control elements which are used in the WER-440 type reactors. The axial division of the moving fuel assembly nodes can change between different time-steps (figure 1). The attached hydraulic channel of the follower always describes the heated part of the channel around the fuel.

Thermohydraulics is calculated in separate axial hydraulic channels, which connect freely to one or several fuel assemblies. Bypass channels of the core can also be included. There is no mixing between the hydraulic channels in the core, which is a good model especially for WER-440 type reactors where there are shroud tubes around individual fuel assemblies.

In order to get an accurate representation of the fuel temperature Doppler feed back the heat transfer calculation with several radial meshes is solved for an average fuel rod in each fuel assembly. The release of prompt and delayed nuclear heat in fuel or in coolant is modelled.

SOLUTION METHODS

The nodal equations of neutronics are solved by a very fast two-level iteration technique as in HEXBU-3D. The accuracy of the method is 1 % in the average assembly powers in the steady state. Core symmetries for full core, half core, 1/3 or 1/6 can be used in the neutronics calculations.

The steady state solution of HEXTRAN is similar to the HEXBU-3D solution except for the influence of the different thermal-hydraulics models. When 8 hydraulic channels were used in HEXTRAN, the deviations in

1/2 multiplication factors were 20 pern at most at different power levels in 1/6 core symmetry calculation of Loviisa. The standard deviations in assemblywise power distributions were 0.2 X (maximum 0.7 X) and in average axial distributions 0.4 X (maximum 0.6 X) between HEXTRAN and HEXBU-3D.

Within homogenized nodes the two group fluxes are represented by linear combinations of two spatial modes, the fundamental and the transient mode of solution. The iteration scheme is based on the fact that the internal shape of the flux within a node is a slowly varying function of the average flux of the node and its neighbours. In the inner neutronic iterations only the average values of the fundamental mode flux are solved. The nodal flux shapes and the coupling coefficients between the neighbouring nodes are improved only during the outer iterations.

During the outer iterations also the feedback effects and thermohydraulics are recalculated. There can also be separate pressure balance iterations of the hydraulics.

Advanced time integration methods are used. Time discretization is made by implicit methods which allow flexible choices of time-steps. In thermohydraulics of the coolant the numerical method for conservation equations can be varied between central difference and fully implicit. The convergence of the calculations is improved when more hydraulic channels are included for assemblies of different power levels.

Channel hydraulics is governed by the conservation equations for steam mass, water mass, total enthalpy, and total momentum, and by appropriate correlations. The mass flow distribution between the channels is based on the pressure balance over the core. The phase velocities may be interconnected by a slip ratio or the drift-flux formalism. The properties of water and steam are represented as rational functions of pressure and enthalpy. The present solution method of hydraulics does not allow flow reversals. In such cases, additional approximations are needed.

The heat conduction equation is solved according to Fourier's law with temperature dependent thermal properties of fuel pellet, gas gap and fuel cladding and with different heat transfer coefficients for different hydraulic regimes.

Hot channel analyses can be carried out with the program TRAB on the basis of auxiliary data files containing HEXTRAN results. These data files including the behaviour of any common variable are made by HEXTRAN during the calculation and they are also used in representing the results graphically.

CONNECTION BETWEEN HEXTRAN AND SMABRE

The thermohydraulics circuit model SMABRE 181 has been dynamically connected to HEXTRAN for the primary and secondary loop calculations. The connection has been made in the similar way as the connection between TRAB and SMABRE in the program SMATRA /9/. The core power distribution in different sectors and levels is transmitted from HEXTRAN to SMABRE and the core inlet conditions of different sectors are transmitted to HEXTRAN.

HEXTRAN can also be used separately as a core model and the core inlet thermohydraulics can be given as disturbances from data files.

1/3 Different connection geometries between HEXTRAN and SMABRE can be defined. The core channels are hydraulically separated. Their number in each program is arbitrary, but their order is supposed to be the same.

The principally different geometries are: 1 only one channel in SMABRE but several channels in HEXTRAN 2 same amount of channels in both the programs 3 whole core symmetry with several channels in HEXTRAN and several channels describing core sectors in SMABRE 4 half core symmetry with several channels in HEXTRAN and several channels describing core sectors in SMABRE.

In case 3 the core sectors of SMABRE do not have to be of the same size. The amount of HEXTRAN channels connected to each SMABRE channel is given in input.

In case 4 also the SMABRE channels have to be determined in the way of half core mirror symmetry. The first SMABRE channel is assumed to be located across both sides of the symmetry line. The rest of the SMABRE channels are symmetrically summed with the others across the symmetry line. The half core symmetry model is useful in analyzing accidents caused by disturbances of one control asssembly or one circuit.

EXAMPLES

Different reactivity initiated accidents (RIA) have been calculated with HEXTRAN (uncontrolled withdrawing of control rod group, ejection of control rods, unintended dilution of soluble boron at the core inlet). The results have been compared against results of the one-dimensional dynamics code TRAB.

Comparative calculations of a hypothetical strong boron dilution transient have been made (figure 2). The dilution in core was radially symmetric. HEXTRAN gives a slightly lower power peak than TRAB as can be postulated for a three-dimensional program. There is no scram included in the calculations and the total powers of the both programs are gradually acquiring steadiness at about the same level.

Examples of control rod movement transients are in figures 3 and 4. In the two first figures of figures 3 the radial assembly power distributions of the scram calculation are shown in the steady state and after 5 seconds. In the last figure of figures 3 there are the ratios of the two distributions. As can be seen the assembly powers of the control rod followers are decreasing especially fast.

In figures 4 again a very hypothetical accident of a control group ejection is shown. The peaks in the last figure of figures 4 demonstrate the large relative power increase in the fuel followers of control assemblies. This analysis has been made with 1/6 symmetry model in the core and less hypothetical analyses with half core symmetry models are being made.

1/4 PLANS FOR HEXTRAN DEVELOPMENT

Present efforts concerning HEXTRAN are concentrated in its applications. Extensive validation work including comparisons with other programs and analyses of radially strongly asymmetric transients. Further studies are needed also for the optimization of the calculational parameters of the program.

REFERENCES

1. R. KYRKI-RAJAMAKI, "HEXTRAN: Three-Dimensional Reactor Dynamics Code for WER-Reactor Cores", Proceedings of the International Topical Meeting on Advances in Mathematics, Computations and Reactor Physics, April 28 - May 2, 1991, American Nuclear Society (1991), pp. 30.2 4- 1-5.

2. E. KALOINEN, R. TERASVIRTA and P. SILTANEN, "HEXBU-3D, a Three-Dimensional PVR-Simulator Program for Hexagonal Fuel Assemblies", Research Report 7/1981, Technical Research Research Centre of Finland, Nuclear Engineering Laboratory, (1981), 148 p + app. 5 p.

3. M. RAJAMAKI, "TRAWA, a Transient Analysis Code for Water Reactors", Report 24, Technical Research Centre of Finland, Nuclear Engineering Laboratory (1976), 149 p + app. 31 p.

4. M. RAJAMAKI, "TRAB, a transient analysis program for BVR, Part 1. Principles", Report 45, Technical Research Centre of Finland, Nuclear Engineering Laboratory (1980), 101 p + app. 9 p.

5. M. ANTILA, R. KYRKI-RAJAMAKI, M. RAJAMAKI, H. RATY, P. SILTANEN and T. VANTTOLA, "Application of the Synthesis Model in an Asymmetric Reactivity Disturbance of the WER-440 Type Loviisa Reactors", Proceedings of the ANS International Topical Meeting on Safety of Thermal Reactors, July 21-25, 1991, American Nuclear Society (1991), pp. 261-268.

6. H. KANTEE, R. KYRKI-RAJAMAKI, J. MIETTINEN, T. VANTTOLA, M. KOMSI and H. TU0MIST0, "Accident Analyses for the Loviisa WER-440 Reactors", Proceedings of the ANS International Topical Meeting on Safety of Thermal Reactors, July 21-25, 1991, American Nuclear Society (1991), pp. 623-630.

7. H. RATY, R. KYRKI-RAJAMAKI and M. RAJAMAKI, "Validation of the Reactor Dynamics Code TRAB", Research Reports 729, Technical Research Centre of Finland (1991), 31 p.

8. J. MIETTINEN, "Development and Assessment of the SBLOCA Code SMABRE", Proceedings of Specialists Meeting on Small Break LOCA Analyses in LWRs, Pisa, Italy, June 23-27, 1985, pp. 481-495.

9. R. KYRKI-RAJAMAKI, "Reactivity initiated accident analyses for Loviisa FSAR with reactor dynamical computation system of VTT", Proceedings of the 19. Symposium on WVER Physics of the VMK. Siofok, Hungary, 30.9. - 6.10.1990. Budapest, 1990. KFKI, pp. 505-519.

1/5 Figure P o w e r(MW) Figure 8000

6000 4000 2000

2. 1.

with Hypothetical Axial

programs

discretization

TRAB boron Large o o • ■

and Core dilution Fission Fission Power Power Fuel Fuel

Control changes

HEXTRAN.

Nodes 1/6 Follower Time Assembly Inlet —

to to

350

Power Power during Assembly accident

Coolant Coolant Boron

ppm (s)

control with with

in without

Disturbance with with

2 TRAB HEXTRAN

assembly seconds

TRAB HEXTRAN scram

movement. calculated

Figure Power Density (MW/m3) 100 150-1 50

4 4 3.

Radial reactor

power scram.

distributions 1/7

and

their Average

ratios

Power

during

Densities

WER-440

of

Assemble

type

Fission power (MW) Power Density (MW/mD) Figure 2000 4000

Control 4.

Hypothetical Control Groun Fission in

0.05

Group Ejection

Time power

seconds

Ejection

of (s) in

control

0.05

seconds

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in

WER-440 Group Group

Power

Ejection Ejection

per

type

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in in

0.05

0

reactor. 05

at State

seconds 0.07 seconds

Power sec Reprinted with permission from the publisher. PAPER II In: Transactions of the ANS Winter Meeting. Washington DC 13-17 November 1994. La Grange Park, IL: American Nuclear Society, 1994. Pp. 473 - 474. (TANSAO 71 1-692.)

RECENT DEVELOPMENT OF VTT'S CALCULATION SYSTEM FOR VVERS

Elja Kaloinen, Markka Anttila & Riitta Kyrki-Rajamaki VTT Energy, Finland

INTRODUCTION

A comprehensive code system for reactor physics and dynamics calculations in hexagonal core geometry has been developed at VTT ENERGY. The main modules of the system consist of the CASMO-HEX assembly burnup code1 and the three-dimensional codes HEXBU-3D (Ref. 2) for burnup sim­ ulation of VVER cores and HEXTRAN (Refs. 3 and 4) for transient and accident analysis of the core and coolant circuit. Figure 1 presents a schematic view of the calculational steps from a nuclear data library to static and dynamic simulations of the reactor. The code system has recently undergone several improvements and modifications, particularly to match the modern requirements for safety analyses. This paper gives a survey of the code system in its present state.

HOMOGENIZED CROSS SECTIONS

CASMO-HEX is an adaptation of an early version of the Swedish code CASMO to hexagonal geometry. Three alterna­ tive modules to calculate the two-dimensional flux distribution within assemblies are designed at VTT. The module based on the transmission probability method is normally used, and the flux is calculated in a region (assembly) of regular hexagonal cells containing fuel or absorber rods or various types of water gaps. Older versions of CASMO-HEX tended to overestimate the absorption in cells of absorber rods. Therefore, a correction factor determined by single-cell calculations was introduced for the flux in absorber cells. Test calculations showed that the cor­ rected results agreed well with results of the CASMO-3G code. Also, the MICBURN code developed by Studsvik Core Analy- sis AB can be used to generate cross-section libraries tor burn­ able absorbers. Thus, CASMO-HEX is capable of calculating all kinds of VVER-440 and VVER-1000 assemblies. Another major improvement to CASMO-HEX is the cal­ culation of flux discontinuity factors for HEXBU-3D. The nodal two-group equations are solved within the assembly cell using the six face-averaged net leakages from the two- dimensional calculation. This gives discontinuity factors simul­ taneously for each face, though some or all of them are usually equal by symmetry. In the case of no net leakage, the factors are simply obtained as ratios of face-averaged to cell-averaged flux.

NODAL CORE CALCULATIONS The three-dimensional two-group code HEXBU-3D solves the flux distribution by a nodal expansion method. The group fluxes are constructed from the fundamental and transient modes of the solution, which are approximated by third-order polynomials and exponential functions within nodes. All rel­ evant feedback effects from fuel and moderator temperature, soluble boron density, and local xenon concentration are described in the code, and the critical boron concentration can be calculated directly as the eigenvalue. The latest version of HEXBU-3D includes the following improvements5:

1. discontinuous flux at transverse interfaces of nodes 2. dependence of cross sections on moderator density history 3. polynomial fitting of individual cross sections in local state variables 4. flexible evaluation of reactivity coefficients by two crit­ icality calculations 5. search of burnup for equilibrium loading (Haling cal­ culation) 6. analysis of moderator disturbances, e.g., boron dilu­ tion. Use of discontinuity factors for standard VVER-440 assemblies offers only a marginal improvement in the results because vari­ ation of the factors by fuel enrichment is small. A more sig­ nificant effect can be expected when assemblies contain strong local absorbers.

II/2 HEXBU-3D has been validated mainly by comparison with measurements from the Finnish Loviisa VVER-440 reactors. The code is routinely used in reload design for these reactors. VVER-1000 benchmarks6 have also been calculated.

DYNAMIC CALCULATIONS

The reactor dynamics code HEXTRAN uses stationary the same neutronics solution method as HEXBU-3D. Advanced time integration methods allow flexible choices of time steps. Now it is possible to make realistic accident analyses starting from accurate core conditions. The SMABRE circuit model7 has been dynamically coupled to HEXTRAN for analyses of accidents in which effects of the whole cooling system are included. The hot channel calculations are made afterward with the TRAB one-dimensional code8 using output files of HEX­ TRAN. Sensitivity studies with different conservatism can eas­ ily be carried out. The extreme phenomena modeled are the

Basic nuclear data

Nuclear data processing

Nuclear data libraries (25 - 70 energy groups) CASMO libraries

Calculation of assemblywise two group constants CASMO-HEX

Calculation of reactivities, power and burnup HEXBU-3D distributions etc.

Data transfer and condensation for one-dimensional CROCO group constants

One-dimensional dynamics codes for core and TRAB, SMATRA related systems

Three-dimensional dynamics code HEXTRAN

C D = codes developed by VTT CD = codes partly developed by VTT CD = codes applied by VTT

Fig. 1. The VTT's calculational system for reactor physics and dynamics.

II/3 fuel temperature rise after occurrence of the boiling crisis and oxidation of the cladding material. The coupled code HEXTRAN-SMABRE has been exten ­ sively used in research on design basis and anticipated accident without scram accidents. The effects of local boron dilution both in operating and shutdown conditions and during acci­ dents are being studied for the Loviisa reactors. Studies on the Russian VVER-91 concept have been going on for several years at VTT in cooperation with IVO International Ltd. In the AGNES project for renewing the safety analyses of the Hun­ garian Paks nuclear power plant, analyses of control rod ejec­ tion accidents and recriticality studies of steam-line-break accidents were performed in Finland.

1. F. WASASTJERNA, E. KALOINEN, R. HOGLUND, M. ANTTILA, “The Nuclear Fuel Management Calculation System of the Technical Research Centre of Finland," Proc. Topi. Mtg. Advances in Fuel Management, North Carolina (1986).

2. E. KALOINEN, P. SILTANEN, R. TERASVIRTA, “Two- Group Nodal Calculation in Hexagonal Fuel Assembly Geometry,” Proc. Specialists' Mtg. Calculation of 3-Dimen- sional Rating Distributions in Operating Reactors, Organi­ zation for Economic Cooperation and Development, Paris (1980).

3. R. KYRKI-RAJAMAKI, “HEXTRAN: Three-Dimensional Reactor Dynamics Code for VVER-Reactor Cores,” Proc. Int. Topi. Mtg. Advances in Mathematics, Computations and Reactor Physics, Pittsburgh, Pennsylvania, April 4- May 5, 1991, p. 30.24-1, American Nuclear Society (1990).

4. R. KYRKI-RAJAMAKI, “Validation of the Reactor Dy­ namics Code HEXTRAN,” STUK-YTO-TR 69, Helsinki (1994).

5. E. KALOINEN, “New Version of the HEXBU-3D Code,” Proc. 2nd Symp. AER for Investigating Neutron Physics and Thermohydraulics Problems of Reactor Safety, Paks, Hungary, September 21-26, 1992, p. 9 (1992).

6. “In-Core Fuel Management Code Package Validation for VVERs," to be published in IAEA-TECDOC series.

II/4 7. J. MIETTINEN, “Development and Assessment of the SBLOCA Code SMABRE,” Proc. Specialists’ Mtg. Small Break LOCA Analyses in LWRs, Pisa, Italy, Vol. 2, p. 481 (1985). 8. M. RAJAMAKI, “TRAB, A Transient Analysis Program for BWR, Part 1. Principles,” Report 45, Technical Research Centre of Finland, Helsinki, Finland (1980).

II/5 Reprinted with permission from the publisher. PAPER III In: Proceedings of the 1993 Simulation Multiconference. Arlington, VA 29 March - 1 April 1993. San Diego, CA: SCS Simulation Series, 1993. Vol. 25, Nro 4. Pp. 18 - 23.

SAFETY ANALYSES FOR VVER TYPE REACTORS WITH THE REACTOR DYNAMICS CALCULATION SYSTEM OF VTT, FINLAND

Riitta Kyrki-Rajamaki and Hanna Raty Technical Research Centre of Finland (VTT) Nuclear Engineering Laboratory P.O.Box 208, SF-02151 Espoo, Finland

ABSTRACT dimensional and axially one-dimensional core dynamics models, connected to a thermohydraulic circuit model for The reactor dynamics calculation system of the the primary and secondary loop calculations. The core Technical Research Centre of Finland (VTT) for VVER models can also be used independently. All the codes reactors is presented with selected examples of safety have been developed in VTT. analyses of VVERs. The three-dimensional reactor dynamics code HEXTRAN developed in VTT accurately The reactor dynamics analyses are supported by the describes the VVER core consisting of hexagonal fuel reactor physics calculation system of VTT. Reactor elements. Main applications of HEXTRAN are physics data for the dynamics codes can be generated asymmetric accidents in the core, such as control rod starting from the basic nuclear data libraries, by using ejection, main steam line break or startup of an inoperable VTT’s hexagonal version of the CASMO code, loop. The axially one-dimensional reactor dynamics code CASMO-HEX, and the three-dimensional stationary nodal SMATRA is intended for applications, where the main fuel management code HEXBU-3D. spatial effects occur in the axial direction, e.g. ATWS. Both codes include a thermohydraulic circuit model for Three-Dimensional HEXTRAN Code the primary and secondary loop calculations. HEXTRAN (Kyrki-Rajamaki 1991) is a three- dimensional hexagonal code for analyses of core transients INTRODUCTION of VVER-440 and VVER-1000 reactors. It is based on the three-dimensional stationary fuel management code In Finland there are 4 nuclear power reactors, two HEXBU-3D (Kaloinen et al. 1981) and on the one- ABB Atom type BWRs in Olkiluoto and two VVER type dimensional reactor dynamics code TRAB (Rajamaki PWRs in Loviisa. A reactor dynamics calculation system 1980). It accurately describes the VVER core consisting for independent safety analyses of both these reactor types has been created in the Technical Research Centre of VTT Nuclear Engineering Laboratory 11 Finland (VTT). The VVER calculation system has been extensively applied to the Loviisa power station (Kantee et REACTOR DYNAMICS CODE DEVELOPMENT al. 1991), to the safety analyses of the new Russian VVER-91 concept, and recently also to the Hungarian TRAB SMATRA VVER-440 power station in Paks. CORE

The main properties of VTT’s reactor dynamics Full BWR Model calculation system for VVER type reactors and selected Full PWR Model SMABRE results of safety analyses for VVERs are presented in this StaL Neutr. paper. HEXTRAN- PWR Circuit HEXBU-3D HEXTRAN VTT’S COMPUTER CODE SYSTEM SMABRE FOR VVER REACTOR DYNAMICS

The reactor dynamics code system of VTT for VVER reactors (Figure 1) consists of both three­ Figure 1 Reactor dynamics code system of VTT of hexagonal fuel elements. HEXTRAN is intended for by the conservation equations for steam mass, water mass, calculation of accidents, where radially asymmetric total enthalpy, and total momentum, and by appropriate phenomena are included and both good neutron dynamics correlations. The mass flow distribution between the and two-phase thermal hydraulics are important. The channels is based on the pressure balance over the core. thermohydraulic circuit model SMABRE (Miettinen 1985) The phase velocities may be interconnected by a slip ratio has been dynamically connected to HEXTRAN for or the drift-flux formalism. The properties of water and analyses of transients where also the thermohydraulics of steam are represented as rational functions of pressure and whole primary and secondary coolant system must be enthalpy. included (e.g. in order to determine the core inlet conditions and system pressure). Different connection In order to get an accurate representation of the fuel geometries between HEXTRAN and SMABRE can be temperature based Doppler feedback the heat transfer defined. calculation with several radial mesh points is made for an average fuel rod in each fuel assembly. The release of The circuit hydraulics solution consists of five prompt and delayed nuclear heat in fuel or in coolant is conservation equations for mass and enthalpy of vapor modelled. The heat conduction equation is solved and liquid and the momentum for the mixture. The phase according to Fourier’s law with temperature dependent separation modelling is based on drift-flux approach. The thermal properties of fuel pellet, gas gap and fuel cladding process description is based on generalized nodes, and with different heat transfer coefficients for different junctions connecting nodes and heat structures describing hydraulic regimes. structure walls, fuel rods and steam generator tubes. Advanced fast non-iterative numerical schemes applying One-dimensional SMATRA code sparse matrix solvers are used for the solution of discretized conservation equations. SMATRA is a wide range accident analysis code which connects dynamically the thermohydraulic circuit In the core models advanced time integration model SMABRE and the one-dimensional core dynamics methods are used. Time discretization is made by implicit model TRAB-CORE. SMATRA is intended for methods which allow flexible choices of time-steps. In applications, where the main spatial effects occur in the thermohydraulics of the core the numerical method for axial direction, e.g. ATWS. conservation equations can be varied between central difference and fully implicit. The thermohydraulics models of the core and the circuit in SMATRA are the same as in HEXTRAN. The The neutron kinetics model of HEXTRAN solves the connection between the core and the circuit model is two-group diffusion equations in homogenized fuel based on the same principles in both codes. assembly geometry by a sophisticated nodal method. Within nodes the two group fluxes are represented by The core dynamics model includes a one-dimensional linear combinations of two spatial modes, the fundamental description of the geometry, neutronics, rod heat transfer, and the transient mode of solution. The dynamic equations and thermal hydraulics, using at most three parallel axial include six groups of delayed neutrons. The feedback channels. In neutron kinetics a synthesis model composed effects from xenon-poisoning, fuel temperature, moderator of a time-dependent axial two group diffusion equation density and soluble boron density are included in the and a radial shape function equation is employed. In the program. A special treatment has been developed for the power excursion transients, the extreme phenomena dynamic calculation of the moving fuel assemblies of big modelled are the fuel temperature rise after occurrence of follower-type control elements which are used in the the boiling crisis and oxidation of the cladding material. VVER-440 type reactors. Core symmetries for full core, half core, 1/3 or 1/6 can be used. The one-dimensional core model of SMATRA (TRAB-CORE) can also be used separately, especially for Thermal hydraulics in the core is calculated in hot channel analyses on the basis of the output files of the separated axial hydraulic channels, which connect freely main calculations made with different codes - HEXTRAN. to one or several fuel assemblies. In VVER-440 type HEXTRAN-SMABRE, SMATRA or TRAB-CORE of the reactors there is no mixing between the hydraulic channels VTT calculation system in Figure 1. in the core because there are shroud tubes around individual fuel assemblies. Channel hydraulics is governed

HI/2 Suitable countermeasures have been implemented in VALIDATION OF THE CALCULATION SYSTEM Loviisa to reduce the probability of such a reactivity accident (Siltanen and Antila 1992). All the codes of the VVER calculation system have been validated against measurements. Initially the reactor is operating at 88 % power, five primary loops running, with core inlet temperature and The methods for generating reactor physics data, and pressure of the loop close to normal. Diluted boron is the steady state results of the reactor dynamics codes have assumed in the hot leg of the isolated primary loop, been validated by thorough comparisons with plant data. because it has the most severe consequences. The amount In stationary state HEXTRAN gives the same results as of dilution is -440 ppm. The reactivity coefficients are HEXBU-3D. conservative estimates from the point of view of boron dilution in the beginning of cycle, when the potential for Validation of the dynamics calculation consists of such a disturbance is highest. It takes about 20 s for the calculation of start-up experiments and real plant boron disturbance in the hot leg to reach the core after the transients, of international benchmark problems and code startup of the loop. The disturbance enters the core comparisons. The three-dimensional kinetics model of stepwise nearly in its full strength at a speed of 3.5 m/s HEXTRAN has been validated by simulations of the (see Figure 2). A sharp and high power peak is obtained spatial kinetics measurements on the Czechoslovak LR-0 (Figure 3). It is limited mainly by the Doppler effect. The test reactor (Kyrki-Rajamaki et al. 1992b). Thermal reactor shutdown is triggered from the power rise, but it hydraulic circuit models have been validated with is not effective until the power peak is already over. calculating eg. international standard problems. Real plant During the power rise axial maximum of the neutron flux transients have been simulated both with BWR and VVER shifts downwards for a moment, but returns close to the models with good accuracy (Raty et al. 1991 and Kyrki- initial distribution at the moment of the largest power. The Rajamaki et al. 1992a). boron disturbance leaves the reactor after three seconds. Pressure of the primary circuit does not rise very much. EXAMPLES OF TYPICAL APPLICATIONS The three-dimensional HEXTRAN and the axially VVER-440 Reactivity Initiated Accidents one-dimensional SMATRA with a two channels synthesis model give compatible results for this strongly radially The first example case is a reactivity initiated asymmetric RIA case. HEXTRAN gives slightly lower accident (RIA) for a VVER-440 type reactor due to an incorrect startup of an isolated primary loop. Coolant with diluted boron from the starting loop suddenly enters the Boron dilution with HEXTRAN and SMATRA reactor core and causes a strong radially asymmetric □ Undisturbed sector power pulse. Analyses have now been carried out with O Disturbed sector HEXTRAN and earlier with SMATRA (Antila et al. 1991). In SMATRA analyses a two channel synthesis model in core and two-dimensional modelling of the downcomer were utilized. In the three-dimensional calculations only the core version of HEXTRAN has been used, and the core inlet values of the SMATRA calculation have been used as disturbances for the HEXTRAN calculation (e.g. the boric acid concentration at core inlet, and the gradually increasing core inlet flow).

In VVER-440 (e.g. in Loviisa) there are main gate 22 23 valves in both the hot and cold legs of all six primary Time (s) coolant loops. Incorrect startup of an isolated loop could potentially lead to a reactivity initiated accident. In such a Figure 2 VVER-440 startup of inoperable loop with - 440 case it is assumed that a loop is not flushed before it is ppm boron disturbance in the hot leg; taken into operation by first switching on the main coolant core inlet boric acid concentration in the pump and then opening the gate valve in the cold leg. disturbed (1/6) and undisturbed (5/6) sectors.

m/3 Radial Riel Temperature Distribution 11 at Time of Maximum Boron dilution with HEXTRAN and SMATRA ucxn

O.. Dist. sector,. SMATRA « ' Bist.'senior HEXTRAN '' & 6 '*' Unciist' sector HEXTRAN IV I i TOO" & 500

300

Time (s)

Figure 3 VVER-440 startup of inoperable loop with - 440 ppm boron disturbance in the hot leg; relative fission power densities in the disturbed (1/6) and undisturbed (5/6) sectors. Figure 4 VVER-440 startup of inoperable loop with - 440 ppm boron disturbance in the hot leg; power peaks than SMATRA as can be expected for a radial assemblywise average fuel temperature three-dimensional program, when the effect of the radial distribution calculated with HEXTRAN. peaking of the Doppler reactivity feedback has not been compensated in the one-dimensional calculation. The relative power densities in the disturbed and undisturbed Disturbed Power per Undisturbed Power sectors of the reactor core are distributed in the same way in the results of both the programs (Figure 3).

Results of the HEXTRAN calculation are illustrated in Figures 4 and 5 as radial assemblywise distributions. In Figure 4 is the radial assemblywise average fuel temperature distribution calculated with HEXTRAN. In Figure 5 is the distribution of the relative power disturbance over the core. It can be seen that the disturbance is concentrated in the 1/6 sector of the core which corresponds to the loop with diluted boron.

VVER-91 ATWS Analyses with SMATRA

ATWS-analyses for the VVER-91 plant concept of WO Atomenergoexport (AEE) have been carried out by VTT in cooperation with IVO International. These analyses were performed with the one-dimensional SMATRA code.

ATWS analyses set high demands to the analysis Figure 5 VVER-440 startup of inoperable loop with - 440 code. The reactor fission power is to be predicted in ppm boron disturbance in the hot leg; extreme conditions differing substantially from the distribution of the relative power disturbance stationary state. The nonlinear reactivity effects are to be over the core calculated with HEXTRAN. included through the two-group diffusion equations. The

m/4 VVER-91 Loss of Feed Water ATWS VVER-91 Loss of Feed Water ATWS

o F\iel center 4) 170 o Pressure A Pellet aver. A Power - v Cladding 160 < - 4000 g

CL 150 3000

- 2000 K

600 600 Time (s) Time (s)

Figure 6 VVER-1000 ATWS; Primary system pressure Figure 7 VVER-1000 ATWS; Maximum fuel and and core fission power calculated by SMATRA. cladding temperatures in the maximum powered fuel rod. complicated circuit hydraulics phenomena are included. neutronics is essential because boiling of the coolant Operator actions are not considered during the first 30 strongly affects the axial neutron fluxes. With present-day minutes of the accident. computer resources it is also possible to perform more time-consuming three-dimensional ATWS analyses, A loss of feed water ATWS case for VVER-91 is including radially asymmetric phenomena and also the shown in Figures 6 and 7 (Kyrki-Rajamaki et al. 1992c). HEXTRAN-SMABRE combination code has been utilized Due to loss of main feed water flow the water level in the in ATWS analyses. steam generators decreases and the reactor coolant pumps are tripped. Reactor power is controlled by the coolant CONCLUSIONS conditions in the core. The water level in the steam generators continues to decrease. With the VVER calculation system of VTT all required reactor dynamics analyses can be done. The The pressurizer safety valves are opened a few times system is thoroughly validated. It has been extensively due to the increased pressure. In the beginning steam is applied for safety analyses of Loviisa VVERs in Finland. leaking out, later water. The maximum pressure is caused ATWS analyses with such initiating events as loss-of- by the rapid volumetric expansion of the primary liquid, feedwater, loss-of-offsite power, control rod group not e.g. by boiling. withdrawal and turbine trip have been calculated. RIA analyses include uncontrolled withdrawals of a control rod Emergency boration of the primary circuit and group and control rod ejection accidents, as well as emergency feedwater injection into the steam generators incorrect startup of an isolated primary loop with colder are activated. The boron injection shuts down the fission water or diluted boron. power within 20 minutes. After that steady conditions prevail until the end of calculation at 30 minutes. In recent years VTT’s VVER calculation system has been increasingly utilized for improving the safety of In the hot channel heat transfer crisis (DNB) occurs VVERs in Eastern Europe, e.g. for safety analyses of the soon after the reactor coolant pumps trip and the fuel and VVER-91 concept, and recently for the Hungarian VVER- cladding temperatures rise. However, there is no local fuel 440 power station in Paks. melting, because the fission power decreases continuously after DNB. The cladding oxidation depth remains also low VTT’s SMATRA code is used also by the Finnish (<1 %) due to moderate cladding temperatures despite the Centre for Radiation and Nuclear Safety (STUK), and the fact that DNB lasts several minutes. Hungarian Atomic Energy Research Institute KFKI AEKI.

In these analyses axially one-dimensional core

III/5 Kyrki-Rajamaki, R.; J. Miettinen; H. Raty; T. Vanttola; REFERENCES N.S. Fil; and P. Siltanen. 1992c. "ATWS analyses for VVER-91 concept by the SMATRA code." In Antila, M.; R. Kyrki-Rajamaki; M. Rajamaki, M.; H. Proceedings of the 3rd Annual Scientific Conference of Raty; P. Siltanen; and T. Vanttola. 1991. "Application of the Nuclear Society International. (St. Petersburg, Russia, the Synthesis Model in an Asymmetric Reactivity Sept 14-18). Nuclear Society International, Moscow, Disturbance of the VVER-440 Type Loviisa Reactors." In Russia 351-354. Proceedings of the ANS Nuclear Reactor Safety Division International Topical Meeting: Safety of Thermal Miettinen, J. 1985 "Development and assessment of the Reactors. American Nuclear Society, La Grange Park, 111., SBLOCA code SMABRE." In Proceedings of the 261-268. Specialists Meeting on Small Break LOCA Analyses in LWRs. University di Pisa, Pisa, Italy, Vol. 2, 481-495. Kaloinen, E.; R. Terasvirta; and P. Siltanen. 1981. "HEXBU-3D, a Three-Dimensional PWR-Simulator Rajamaki, M. 1980. "TRAB, a transient analysis program Program for Hexagonal Fuel Assemblies". Research for BWR, Part 1. Principles." Report 45. Technical Report 7/1981. Technical Research Research Centre of Research Centre of Finland, Nuclear Engineering Finland, Nuclear Engineering Laboratory, Helsinki, Laboratory, Helsinki, Finland. Finland. Raty, H.; R. Kyrki-Rajamaki; and M. Rajamaki. 1991. Kantee, H.; R. Kyrki-Rajamaki; J. Miettinen; T. Vanttola; "Validation of the reactor dynamics code TRAB." M. Komsi; and H. Tuomisto. 1991. "Accident Analyses Research Report 729. Technical Research Centre of for the Loviisa VVER-440 Reactors." In Proceedings of Finland, Nuclear Engineering Laboratory, Espoo, Finland. the ANS Nuclear Reactor Safety Division International Topical Meeting: Safety of Thermal Reactors. American Siltanen, P.; and M. Antila. "Extended Protection Against Nuclear Society, La Grange Park, 111., 623-630. Reactivity Accidents Caused by Slugs of Diluted Water in the Loviisa Reactors." In Proceedings of the 2nd Kyrki-Rajamaki, R. 1991. "HEXTRAN: Three- symposium of AER (Atomic Energy Research) for Dimensional Reactor Dynamics Code for VVER-Reactor Investigating Neutron Physics and Thermohydraulics Cores." In Proceedings of the International Topical Problems of Reactor Safety. (Paks, Hungary, Sept. 21-26). Meeting on Advances in Mathematics, Computations and KFKI Atomic Energy Research Institute, Budapest, Reactor Physics. (Pittsburgh, VA, Apr. 4-May 5). Hungary, 327-342. American Nuclear Society. LaGrange Park, 111, 30.2 4-1 - 30.2. 4-5. BIOGRAPHIES

Kyrki-Rajamaki. R.; J. Miettinen; H. Raty; and T. Ms. Riitta Kyrki-Rajamaki is a senior research scientist Vanttola. 1992a. "Validation of SMATRA accident and leader of the reactor physics section in the Nuclear analysis code against Loviisa plant data" In Proceedings Engineering Laboratory of the Technical Research Centre of the 3rd International Symposium on Power Plant of Finland (VTT). Her past experience includes Transients - 1992 ASME Winter Annual Meeting. development, testing, validation and application of VTT’s (Anaheim, CA, Nov. 8-13). American Society of reactor dynamics codes, and conducting safety analyses Mechanical Engineers. New York, NY, FED-Vol. 140, for both BWR and VVER reactors. She is currently 153-162. working on three-dimensional core dynamics modelling. Ms. Kyrki-Rajamaki has a MSc in Technical Physics from Kyrki-Rajamaki, R.; H. Raty; T. Slcnius; and T. Vanttola. the Helsinki University of Technology. 1992b. "Validation cases of HEXTRAN and SMATRA reactor dynamics codes - comparative calculations and Ms. Hanna Raty is a senior research scientist in the simulations of LR-0 ;md Loviisa plant data" In Nuclear Engineering Laboratory of VTT. Her past Proceedings of the 2nd symposium of AER (Atomic experience includes development, testing, validation and Energy Research) for Investigating Neutron Physics and application of VTT’s reactor dynamics codes, and Thermohydraulics Problems of Reactor Safety. (Paks, conducting safety analyses for both BWR and VVER Hungary, Sept. 21-26). KFK1 Atomic Energy Research reactors. Ms. Raty has a MSc in Technical Physics from Institute, Budapest, Hungary, 105-117. the Helsinki University of Technology.

m/6 Reprinted with permission from the publisher. PAPER IV Helsinki: Finnish Centre for Radiation and Nuclear Safety, 1994. 24 p. (STUK-YTO-TR 69.)

Validation of the reactor dynamics code HEXTRAN

Riitta Kyrki-Rajamaki VTT ENERGY Nuclear Energy

In the Finnish Centre for Radiation and Nuclear Safety the study was supervised by Keyo Valtonen

This study was conducted at request of the Finnish Centre for Radiation and Nuclear Safety

FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY P.O.BOX 14, FIN-00881 HELSINKI, FINLAND Tel. +358-0-759881 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

KYRKI-RAJAMAKI, Riitta (Technical Research Centre of Finland, VTT). Validation of the reactor dynamics code HEXTRAN. STUK-YTO-TR 69. Helsinki 1994. 24 p.

ISBN 951-47-9321-8 ISSN 0785-9325

Keywords: nuclear safety, WWER type reactors, three-dimensional reactor dynamics, hexalgonal kinetics, accident analyses, validation

ABSTRACT

HEXTRAN is a new three-dimensional, hexagonal reactor dynamics code developed in the Technical Research Centre of Finland (VTT) for WER type reactors. This report describes the validation work of HEXTRAN. The work has been made with the financing of the Finnish Centre for Radiation and Nuclear Safety (STUK). HEXTRAN is particularly intended for calculation of such accidents, in which radially asymmetric phenomena are included and both good neutron dynamics and two-phase thermal hydraulics are important.

HEXTRAN is based on already validated codes. The models of these codes have been shown to function correctly also within the HEXTRAN code. The main new model of HEXTRAN, the spatial neutron kinetics model has been successfully validated against LR-0 test reactor and Loviisa plant measurements. Connected with SMABRE, HEXTRAN can be reliably used for calculation of transients including effects of the whole cooling system of VVERs.

Further validation plans are also introduced in the report.

IV/2 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

KYRKI-RAJAMAKl, Riitta (VTT Energia). Reaktoridynamiikkaohjelman HEXTRAN kelpoistaminen. STUK-YTO-TR 69. Helsinki 1994. 24 s.

ISBN 951-47-9321-8 ISSN 0785-9325

Avainsanat: ydinvoimaloiden turvallisuus, WER-reaktorit, kolmidimensioinen reaktoridynamiikka, heksagonaalinen kinetiikka, onnettomuusanalyysit, kelpoistaminen

TIIVISTELMA

HEXTRAN on uusi Valtion teknillisessa tutkimuskeskuksessa (VTT) kehitetty kolmiulotteinen reaktoridynamiikkaohjelma. Tassa raportissa kuvataan HEXTRANin kelpoistamista, joka on suoritettu Sateilyturvakeskuksen (STUK) rahoituksella. HEXTRAN on tarkoitettu WER-tyyppisten kuusikulmiohilaisten painevesireaktoreiden laskentaan. Se soveltuu erityisesti sellaisten onnettomuus- ja bairiotilanteiden simulointiin, joissa esiintyy radiaalisesti epasymmetrisia hairidita ja joissa seka neutronidynamiikan etta kaksifaasitermohydrauliikan tarkka kuvaaminen on tarkeata.

HEXTRAN on kehitetty jo aiemmin perusteellisesti kelpoistettujen ohjelmien pohjalta. On osoitettu, etta naista otetnt mallit toimivat oikein myos HEXTRANissa. Tarkein HEXTRANin uusi malli, paikkariippuvan neutronikinetiikan malli on menestyksellisesti kelpoistettu tsekkilaisen LR-0 testireaktorin ja Loviisan laitoksen mittausten avulla. HEXTRANiin on myos kytketty piirimalliksi VTT:n ohjelma SMABRE. Tata yhdistelmaohjelmaa voidaan luotettavasti kayttaa sellaisten transienttien laskentaan, joissa tarvitaan koko jaahdytysjarjestelman kuvausta.

Raportissa kerrotaan myos HEXTRANin kelpoistuksen jatkosuunnitelmista.

IV/3 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

CONTENTS

Page ABSTRACT

THVISTELMA

1 INTRODUCTION 7

2 STEADY STATE VALIDATION 9

3 VALIDATION OF THE NEW SPATIAL KINETICS METHOD 11 3.1 LR-0 test reactor measurements 11 3.2 Loviisa 2 start-up experiment 16

4 COMPARISON CALCULATIONS WITH TRAB 17

5 HEXTRAN-SMABRE COMBINATION CODE 20

6 FURTHER VALIDATION PLANS 21

7 CONCLUSIONS 22

REFERENCES 23

IV/4 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

1 INTRODUCTION

HEXTRAN 11-31 is a new three-dimensional , It accurately describes the WER core consisting hexagonal reactor dynamics code developed in of hexagonal fuel elements and one-dimensional the Technical Research Centre of Finland (VTT) flow channels. The thermohydraulic circuit for WER type reactors. This report describes model SMABRE /10/ has been dynamically the validation work of HEXTRAN. The work has connected to HEXTRAN for analyses of been made with the financing of the Finnish transients where also the thermo-hydraulics of the Centre for Radiation and Nuclear Safety whole primary and secondary coolant system (STUK). must be included (eg in order to determine the core inlet conditions and system pressure). HEXTRAN is intended for calculation of accidents, particularly when radially asymmetric The reactor dynamics code system of VTT for phenomena are included and both good neutron WER type reactors can be seen in Figure I. dynamics and two-phase thermal hydraulics are HEXTRAN and the combination code important. It is based on the three-dimensional HEXTRAN-SMABRE are based on all the stationary code HEXBU-3D /4,5/ and on the one ­ development work of VTT in this field. Many of dimensional reactor dynamics code TRAB /6-9/. the models used in HEXTRAN are the same

REACTOR DYNAMICS CODE DEVELOPMENT

TRAB SMATRA CORE

Full BWR Model Full PW =1 Model SMABRE Stat. Neutr. HEXBU-3D HEXTRAN HEXTRAN- Circuit SMABRE

Figure 1.

IV/5 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69 as in the codes on which it is based and which of the code has been checked by comparing its have already been thoroughly validated. results with results of other codes - in stationary Therefore die validation work of HEXTRAN has state with HEXBU-3D, in dynamics with TRAB been concentrated on the new models of and in circuit calculations with SMABRE and HEXTRAN, especially on the spatial kinetics SMATRA/11/. model. In addition to that the overall functioning

IV/6 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

2 STEADY STATE VALIDATION

In steady state HEXTRAN has been validated The HEXTRAN thermohydraulics model would against HEXBU-3D calculations for the Loviisa be very accurate if each fuel assembly could be power station. HEXBU-3D and its data base have connected to an own flow channel. However, for been thoroughly validated against Loviisa reasons of computer capability this has not been measurements /12,13/ and against fine mesh practical so far. The assemblies connected to the calculations with the code TRICON /14,15/. same flow channel must be chosen carefully.

The HEXTRAN solution of neutronics in steady In Table I (next page) are some comparisons with state is in principle the same as in HEXBU-3D. HEXBU-3D results. They concern the effects of The only difference is handling of the varying thermohydraulic modelling in thermohydraulic feedback effects. In HEXBU-3D HEXTRAN. As can be seen the radial power this is based on simple correlations which depend distribution is more accurate when the number of on the power level of the nodes. In HEXTRAN flow channels is increased. On the other hand, complete radial heat transfer models of fuel and the multiplication factor and axial power cladding and axial hydraulics models of flow distribution are more sensitive to the correct channels are included. value of gas gap resistance - in the last case the average fuel temperatures of the whole core are At low power levels no thermohydraulic feedback the same in results of both the codes. effects are included and it has been checked that the results of both the codes are the same. Such quantities which are not especially dependent on The differences between HEXTRAN and temperature are also predicted very similarly HEXBU-3D results are smaller or of the same with both the codes (eg differences in the magnitude as the measurement errors of Loviisa stationary control rod reactivity values are less measurements. than 1CT4, only a few perns).

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Table I. Comparison ofHEXBU-3D and HEXTRAN results at nominal powerin beginning of cycle 13 ofLoviisa 1. Effects of different models in thermohydraulics of HEXTRAN. (Neutronics calculated with 1/6 symmetry in core: 53 fitel assemblies and 10 axial node layers)

Calculations! case Effective multi­ Maximum Standard Maximum Standard of HEXTRAN plication factor deviation of deviation of deviation of deviation of thermohydraulics ( HEXBU-3D relative relative average average value 1.0000) assembly assembly axial node axial node powers (%) powers (%) powers (%) powers (%)

Number of flow 0.9982 0.9 0.4 1.2 0.8 channels 2, gas gap resistance 3.8 KAVcm2

Number of flow 0.9980 0.5 0.2 1.1 0.8 channels 8, gas gap resistance 3.8 KAVcm2

Number of flow 0.9998 0.7 0.2 0.6 0.4 channels 8, gas gap resistance 3.0 KAVcm2

IV/8 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

3 VALIDATION OF THE NEW SPATIAL KINETICS METHOD

3.1 LR-0 test reactor Additionally, based on experience with Loviisa and WER-1000 simulations, a transient mode measurements correction of HEXTRAN/HEXBU-3D was tested, the range of C value was from 0.5 (the Space-time kinetic experiments were carried out value used in Loviisa WER-440) to 1.0 (no on the Czechoslovakian LR-0 zero power test correction). The need for the correction is not as reactor during 1986-1988 and subsequently used large in the large WER-1000 assemblies as in for validation of the three-dimensional German VVER-440s and the value of 0.75 was finally reactor kinetics code DYN3D/M1 /16, 7/. Now used. these experiments have been simulated also with HEXTRAN /18/. Some of the detectors in LR-0 are situated in the fuel assemblies with the moving absorber The experiments on the LR-0 test reactor were clusters. When a cluster is inserted this detector performed in fuel assembly configurations with becomes surrounded by the absorption rods, either 31 or 55 shortened (height 125 cm) fuel which results in a local flux depression in the assemblies of VVER-1000 type. Different detector position, in addition to the decrease of enrichments from 2 to 4.4 % were used. Both the mean flux of the assembly. Therefore a fine symmetric and eccentric time-dependent mesh correction for this detector was employed reactivity perturbations were induced by also in HEXTRAN comparisons, taking into movements of an experimental cluster of 18 account a flux depression of 9.4 %. absorber elements. The simulated cases include both relatively slow reactivity perturbations with In the first measurement the LR-0 core consists the cluster moving in and out of the core, and of 31 fuel assemblies. An eccentrically located relatively fast perturbations with the cluster experimental cluster (EC2 in Figure 2) is first dropped into the core. Waterproof fission micro chambers situated in the central tube of different fuel assemblies were used for the neutron flux detection.

The simulations with HEXTRAN were carried out in order to validate the new neutron kinetics model of the code. The additional validation of the method for generation of neutron physics data for the neutronics model was excluded from the work at this stage. German data were used for homogenized two group constants and delayed neutrons. Boundary conditions for the radial reflector in HEXTRAN as an albedo matrix were calculated on the basis of the radial power distributions of the two-dimensional diffusion code TRICON /15/, which used two group cross Figure 2. LR-0 core with 31 juel assemblies: section data for the radial reflector. Die correct locations of the experimental clusters (EC) and representation of the boundary conditions was the detectors at different axial levels essential for this small experimental core. (C=central, U=upper).

IV/9 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

HEXTRAN Calculation Results HEXTRAN Calculation Results against against LR-0 Reactor Measurement 1 LR-0 Reactor Measurement 1

LEGEND LEGEND a Calc of Pet C3 04 • a Calc, of Pet. C22 o Calc: of Pet CIO o Calc, of Pet. UlY v Calc’ of Pet Cl3 ? Calc, of Pet. C14 Measurements Measurements

Time (s) Time (s)

Figure 3, Figure 4.

HEXTRAN Calculation Results against LR-0 Reactor Measurement 2

CLIO

03 ■ LEGEND ? Calc, of Pet. C13 Measurements

Time (s)

Figure 5. LR-0 core with 55 fuel assemblies: Figure 6. locations of the experimental clusters (EC) and the detectors at different axial levels detector locations, which can be found in (U=upper, C=central, CL —central-lower, Figure 2 (page 11). The calculated and measured L = lower). values are in very good agreement.

slowly inserted 24 cm deeper into the core at In the rest of the measurements the LR-0 core constant speed, and after a holding time had 55 fuel assemblies with five different fuel withdrawn 24 cm from the core with constant enrichments (Figure 5). There were detectors speed, following a trapezoidal shape of also outside the active core, but their disturbance. Figures 3 and 4 show the measurement results are not compared here, comparisons of relative detector rates calculated because the reflector area was not included in by HEXTRAN for different axial and radial HEXTRAN as ordinary nodes.

IV/10 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

In the second measurement, still a slow movement and at the end of the calculation. Both perturbation, the eccentrically located the local effect of the moving cluster and the experimental cluster (EC2 in Figure 5) was effect on the whole power level can clearly be moved down and up again in the core. Figure 6 seen. It can also be seen in this small LR-0 core shows the comparison of the calculated and that there are large differences between the measured values of relative detector rate at the power levels of assemblies due to different location of the experimental cluster (see Figure enrichments. The transient correction (C 5). The values are almost identical. 0.5...1.0) had nearly no effects on the behaviour of the relative dynamic flux rates, but it changed In Figure 7 are the radial power distributions at die absolute flux levels of the assemblies. different times just before and after the cluster

Figure 7. Radial fission power distributions at different times of LR-0 reactor measurement 2 with 55 fuel assemblies

IV/11 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

HEXTRAN Calculation Results HEXTRAN Calculation Results against against LR-0 Reactor Measurement 4 LR-0 Reactor Measurement 3 08 ■ 0.8 r

LEGEND LEGEND a Calc, of Pet U12 o Calc, of Pet. C7 o Calc of Pet " Calc of Pet. C6 7 Calc of Pet Measurements Mea s u r e me nt s

00 t Time (s) Time (s)

Figure 8. Figure 9.

In the measurement 3 the centrally located locations, which can be found in Figure 5 (page experimental cluster (EC1 in Figure 5, page 12) 12). was slowly moved 40 cm downward. In Figure 8 are the results for two detectors which are near In Figure 11 relative detector rates for the very the cluster EC1. The calculated results very short time period of the actual rod drop are closely agree with the measured values. shown. Results of three detectors located at different axial levels in the core (see Figure 5) In the measurements 4 and 5 fast perturbations of are given. As can be seen in Figure 11 the a rod drop were induced. There were detectors at disturbance affects the lower part of the core four different heights in the core. In die fourth later. However, the fluxes at detectors U14 and measurement a centrally located absorber cluster L19 gradually achieve the same level because (EC2 in Figure 5) was dropped from a half-way their distance from the disturbance at EC2 is the inserted to fully inserted position in about 2 same (see Figure 5). All the calculated results are seconds. Also this fast disturbance with large again in very good agreement with the axial and radial flux deformations was accurately experimental values. predicted with HEXTRAN as can be seen in Figure 9 where results for three detectors at Some information about all the measurements are different axial and radial locations are shown. collected in Table II. In Table II are also the calculated and measured steady state reactivities. In the fifth measurement an eccentrically located They agree well with the experiments, in all the absorber cluster (EC2 in Figure 5) is dropped cases within the measurement accuracy, which into die core from the fully withdrawn to the fully includes only the differences between detectors. inserted position in less than 2 seconds. Figure The changing of the transient correction (C 10 shows the comparison of relative detector 0.5... 1.0) had an effect of ± 0.1...0.9 cent on rates calculated by HEXTRAN in three detector the steady state reactivity.

IV/12 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

Table 11. Comparison of experimental and calculated reactivities for Jive measurements of kinetic experiments at LR-0 reactor______

Measurement 1 2 3 4 5 Number of assemblies 31 55 55 55 55 Perturbation eccentric eccentric central central eccentric Range of moving cluster 78.7- 84.5- 83.3- 74.9- 125.0 - height (cm) 54.7 44.5 43.3 1.9 1.9 Velocity of exp. cluster 3 2.7 2.7 34 70 (cm/s)

Experimental reactivity -18.7 -21.7 -58.7 -57.7 -38.1 (cent) ± 1.7 ± 1.7 ± 6.3 + 4.4 ± 2.1 Calculated reactivity, -19.2 -21.4 -52.4 -62.0 -38.1 HEXTRAN (cent)

Calculated reactivity, -19 -21.5 -55 -65.4 -37.7 DYN3D/M1 (cent)

HEXTRAN Calculation Results against ( HEXTRAN Calculation Results against ^ LR-0 Reactor Measurement 5 i LR-0 Reactor Measurement 5

LEGEND LEGEND a Calc of Pet C3 a Calc of Del. U34 o Calc, of Pet Cl 6 o Calc, of Pet. CI5 v Calc of Pet Cl 3 7 Calc of'Dei Ll§ Measurements Me a s u rements

06 •

Time (s) Time (s)

Figure 10. Figure 11.

All the five LR-0 experiments were simulated different codes closely agree with each other, and with HEXTRAN with excellent accuracy. The their deviations from the measured values are dynamic effects at different radial and axial core always in the same direction. locations were well predicted. The calculated relative detector rates closely agree with both the Both die time- and space-dependent dynamic experimental values and even better with die effects due to slow and fast perturbations, and the results calculated with DYN3D/M1. It is steady state reactivities of die documented LR-0 noteworthy that the results of die two quite experiments are very accurately calculated by HEXTRAN.

IV/13 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

3.2 Loviisa 2 start-up used as disturbances in the HEXTRAN calculation. As can be seen in Figure 12, the core experiment powers calculated by HEXTRAN and SMATRA in this radially symmetric case were so similar The LR-0 measurements were made with WER- that there was no need for a new circuit 1000 finger type control rods. In WER-440 type calculation. reactors, eg in Loviisa, the control rods are big follower-type control elements. A special A model of Loviisa beginning of life core was treatment has been developed in HEXTRAN for prepared for HEXTRAN. The core was modelled the dynamic calculation of the moving fuel in a 1/6 symmetry with 59 fuel elements of actual follower assemblies connected to this type of enrichments and zero burnup. Axially 10 layers control elements. In order to validate this model, were used both in neutronics and a calculation was made against measurement of thermohydraulics which was modelled using 15 die Loviisa 2 start-up experiment of reactor trip. flow channels. Best estimate reactor physics cross In a reactor trip all the control elements are sections and kinetics parameters (neutron simultaneously dropped into the core and more velocities and delayed neutron fractions) were than 10 % of the fuel is at the same time removed used which were calculated by VTT's hexagonal from the active core. Thus a good test for the version of the CASMO code, CASMO-HEX model of moving fuel is created. /20/. Boundary conditions of control elements and core edges were the best estimate values for Recently simulations with SMATRA against Loviisa without dummy fuel assemblies. Loviisa plant data were carried out in order to supplement the validation of the code. The model In Figure 13 are the fission power measurement and final results of the simulations are described of Loviisa 2 startup experiment and the in detail in reference 19. Reactor trip at full calculation result of HEXTRAN drawn in power was simulated very well. Some results of logarithmic scale. A very accurate simulation can the SMATRA simulation were utilized in be seen. The HEXTRAN result was achieved HEXTRAN calculation. The time dependent core with no modification or tuning of the model. inlet conditions calculated by SMATRA were

Lovnsa 2 start-up experiment. Lovuse Z start-up experiment REACTOR TRIP from IOC % power REACTOR TRIP from 100 % power

o Measurement Calc HEXTRAN C Measurement Calc HEXTRAN

30 Time (s) Time (s)

Figure 12. Figure 13.

IV/14 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

4 COMPARISON CALCULATIONS WITH TRAB

The overall dynamic behaviour of HEXTRAN shown here between HEXTRAN and SMATRA has been checked against TRAB, results of which for the Loviisa WER-440 type reactors. The have been validated against real BWR transients. core model of SMATRA is the same as in There are two reasons for this decision. Firstly, TRAB. there are no direct measurements of real plant transients of eg large power increases at WER The example transient is a reactivity initiated type reactors. Furthermore, no international accident due to an incorrect startup of an isolated benchmark problems have been available for primary loop which included diluted boron. hexagonal three-dimensional dynamics codes. Coolant with diluted boron from the starting loop Secondly, many models of HEXTRAN are the suddenly enters the reactor core and causes a same or similar as in TRAB, and in order to strong asymmetric power pulse. The axially one­ validate them, it is sufficient to check their dimensional calculations with SMATRA, utilizing proper functioning in the new environment. the two channels synthesis model of TRAB and two-dimensional modelling of the downcomer, In HEXTRAN the thermal hydraulics in the core have been thoroughly described in reference 22. is calculated with separated axial hydraulic channels, which connect freely to one or several fuel assemblies. The channel hydraulics is Initially the reactor is operating at 88 % power, calculated with the same models as in TRAB five primary loops running, with core inlet where also a few parallel channels can be defined temperature and pressure of the loop close to in the core. The heat transfer calculation of fuel normal. Diluted boron is assumed in the hot leg and cladding with several radial mesh points is of the isolated primary loop, because it has the made for an average fuel rod in each fuel most severe consequences. The amount of assembly in HEXTRAN. In principle these dilution is - 440 ppm. The reactivity coefficients models are the same as in TRAB, only the are conservative estimates from the point of view geometry is changed. of boron dilution in the beginning of cycle, when the potential for such a disturbance is highest. It TRAB has been thoroughly validated against takes about 20 s for the boron disturbance in the measurements of real plant data, start-up hot leg to reach the core after the startup of the experiments and actual transients, and with loop. The disturbance enters the core stepwise calculations of several international benchmark nearly in its full strength at a speed of 3.5 m/s. A problems and independent code comparisons sharp and high power peak is obtained. It is /21/. limited mainly by the Doppler effect. The reactor shutdown is triggered from the power rise, but it Different radially symmetric reactivity initiated is not effective until the power peak is already accidents (RIA) have been calculated with over. During the power rise axial maximum of HEXTRAN (uncontrolled withdrawing of control the neutron flux shifts downwards for a moment, rod group, ejection of control rods, unintended but returns close to the initial distribution at the dilution of soluble boron). The results have been moment of the largest power. The boron consistent with the results of TRAB. disturbance leaves the reactor after three seconds. Pressure of the primary circuit does not rise very As an example, a comparative calculation of much. radially asymmetric boron dilution transient is

IV/15 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

In this calculation only the core version of increase in die core. The minor peaks and valleys HEXTRAN has been used, and the core inlet in the otherwise smooth behaviour of the relative values of the SMATRA calculation have been power increase distributions show the effects of used as disturbances for the HEXTRAN the deviating geometry of the control element calculation (eg the boric acid concentration at followers. Seven of the control elements are core inlet of Figure 14, and the gradually partially inserted and their followers are thus increasing core inlet flow). partially under the core, and all the followers are shorter than the normal fuel assemblies. There HEXTRAN gives a slightly lower power peak are strong axial deformations in the fission power than SMATRA as can be expected for a three- due to the boron dilution front passing through dimensional code, when the effect of the radial the core. Their effects on the axially averaged peaking of the Doppler reactivity feedback has powers of the fuel followers are slightly different not been fully compensated in the one­ than the effects on the normal fuel assemblies. dimensional calculation with only two radial regions. Also the relative power densities in the The three-dimensional HEXTRAN and the disturbed and undisturbed sectors of the reactor axially one-dimensional SMATRA with a two core are distributed in die same way in the results channels synthesis model give compatible results of both the codes (Figure 15). for this strongly radially asymmetric RIA case.

In Figure 16 are some radial distributions of The comparison shows that the models of assemblywise average values calculated with HEXTRAN are functioning correctly and eg the HEXTRAN at die time of the maximum power flow channel distribution of HEXTRAN was peak (21.2 s) and a little later at the time of the reasonably chosen (19 flow channels connected maximum fuel temperature (22.8 s); notice that with 166 ftiel assemblies in a half core symmetry they are not drawn to the same scale. At the top model). The comparison also gives additional of the page are the fission power density proof of the applicability of the synthesis model distributions and the lowest figures are the fuel for analyzing radially asymmetric transients, temperature distributions. In the middle of the earlier confirmed with thorough comparisons page are the distributions of relative power with HEXBU-3D stationary calculations.

00 11 0 \ Boron dilution with HEXTRAN and SMATRA. Boron dilution with HEXTRAN and SMATRA or 105 O Undisturbed sector y 10 0 D Disturbed sector o o 95 -O . Dist, sector. SMATRA „_„_ •o l / • Dist sector. HEXTRAN o 90 .9.. Undist sector,. SMATRA < •1 '■ ' Undist sector. HEXTRAN o 8.5 1 c l a 80 | % 75 ^------J 7 0 E O u 20 21 22 23 24 25 Time (s) Time (s)

Figure 14. Figure 15.

IV/16 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

Radial Fission Power Distribution Radial Fission Power Distribution at Time of Maximum 2501

1501

lOOl

Disturbed Power per Undisturbed Power Disturbed Power per Undisturbed Power at Time of Maximum Temperature at Time of Maximum Power Peak 31 with HEXTRAN with HEXTRAN

(2 zl I I

Radial FUel Temperature Distribution at Time of Maximum Power Peak

Figure 16.

IV/17 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

5 HEXTRAN-SMABRE COMBINATION CODE

The thermohydraulic circuit model SMABRE has applications calculated with RELAP5/Mod2 in been dynamically connected to HEXTRAN for parallel and participation in many international calculations where the whole primary and standard problems arranged by OECD and secondary coolant system is included 1231. The IAEA. combination code is called HEXTRAN- SMABRE. In HEXTRAN-SMABRE the thermo ­ Recently, dynamic simulations of real Loviisa hydraulics is calculated with SMABRE for the plant data with SMATRA, consisting of a trip of whole coolant system and related subsystems. two main circulation pumps, trip of one turbine, The neutronics, the heat transfer equations of fuel reactor trip and an over cooling transient were and cladding and the core hydraulics are solved carried out /19 /. In the simulations the emphasis with HEXTRAN. was on the thermal-hydraulic behaviour of the primary loop. The connection between HEXTRAN and SMABRE is based on the same principles as in The SMATRA code and the applied plant SMATRA /11/. It is of course more complicated description proved to simulate reliably the and different connection geometries can be calculated basic transients of the Loviisa defined. The coupling of the codes was checked VVER-440 type nuclear power plant. The by calculating the same cases with both behaviour of die main parameters, such as fission HEXTRAN-SMABRE and SMABRE. power, temperatures, pressures and flow rates, were predicted with reasonable accuracy without HEXTRAN-SMABRE validation is based on major modifications in the model. The success of HEXTRAN and SMABRE validations, because especially the reactor trip simulation indicates SMABRE and HEXTRAN codes are used that the code and the plant description properly unchanged within the combined code. Also the reproduces the basic heat transfer chain from the efforts made for validation of SMATRA code can fuel through die steam generators to the discharge directly be utilized in the work with HEXTRAN- from the secondary circuit in the normal SMABRE, because the SMABRE part and the operation range of the plant. The pump connection principles are the same. characteristics was seen to need a more accurate description in such cases where only some of the The validation of the SMABRE primary and pumps are tripped. Therefore a more accurate secondary circuit model includes some analyses pump model (similar to the model used eg in of real plant events, experience from different TRAB or RELAP) was added into SMABRE.

IV/18 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

6 FURTHER VALIDATION PLANS

The LR-0 measurements were excellently The interpretation of dynamic control rod worth simulated with HEXTRAN by using the German measurements eg in Loviisa or Paks (Hungary) data. The reactor dynamics analyses are stations creates also a challenge to a three- supported by the reactor physics calculation dimensional dynamics code. system of VTT. Also the method of evaluation of the cross sections and especially the kinetics In AER (Atomic Energy Research for parameters with CASMO-HEX could be Investigating Neutron Physics and validated against these measurements if Thermohydraulics Problems of Reactor Safety) corresponding data were generated in Finland new hexagonal three-dimensional kinetics starting from the basic nuclear libraries. benchmark problems have been defined which simulate a WER-440 core. These problems and Kinetics measurements have also been performed future dynamics benchmark problems of AER are in Russian test reactors and their simulation could utilized for the HEXTRAN validation. be useful in the validation work of HEXTRAN.

IV/19 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

7 CONCLUSIONS

HEXTRAN is based on already validated codes. validated against LR-0 test reactor and Loviisa The models of these codes have shown to plant measurements. function correctly also within the HEXTRAN code. Connected with SMABRE, HEXTRAN can be reliably used for calculation of transients The main new model of HEXTRAN, die spatial including effects of the whole cooling system of kinetics model has been successfully VVERs.

IV/20 FINNISH CENTRE FOR RADIATION STUK-YTO-TR 69 AND NUCLEAR SAFETY

REFERENCES

1. Kyrki-Rajamaki R. Kolmidimensioisen 6. Rajamaki M. TRAB, a transient analysis dynamiikkaohjelman kehittaminen WER- program for BWR, Part 1. Principles. tyyppiselle painevesireaktorille (Deve­ Helsinki 1980. Technical Research Centre lopment of a Three-Dimensional Dynamics of Finland, Nuclear Engineering Code for WER-type PWRs). Finnish Laboratory, Report 45. 101 p + app. 9 p. Centre for Radiation and Nuclear Safety, STUK-YTO-TR 20. Helsinki 1990: 17 p. + 7. Rajamaki M. TRAWA, a transient analysis app. code for water reactors. Technical Research Centre of Finland, Nuclear Engineering 2. Kyrki-Rajamaki R. HEXTRAN: Laboratory, Report 24. Espoo 1976: 149 p Three-Dimensional Reactor Dynamics Code + app. 31 p. for WER-Reactor Cores. Proceedings of the International Topical Meeting on 8. Raiko R (currently Kyrki-Rajamaki R), Advances in Mathematics, Computations Rajamaki M. TRAWA, a transient analysis and Reactor Physics. Pittsburgh, USA, 28.4 code for water reactors, Supplementary part - 2.5.1991. American Nuclear Society. 1. Technical Research Centre of Finland, LaGrange Park 1991: 30.2 4-1-30.2. 4-5. Nuclear Engineering Laboratory, Report 33. Helsinki 1978: 54 p. 3. Kyrki-Rajamaki R. HEXTRAN: VVER Reactor Dynamics Code for 9. Raty H, Rajamaki M. TRAB, a transient Three-Dimensional Transients. Proceedings analysis program for BWR, Part 2. User's of the 1st symposium of AER (Atomic manual. Technical Research Centre of Energy Research) for Investigating Neutron Finland, Nuclear Engineering Laboratory, Physics and Thermohydraulics Problems of Research Notes 1232. Espoo 1991: 105 p + Reactor Safety. Rez, Czechoslovakia, 23. - app. 46. 27.9.1991. KFKI (Central Research Institute for Physics of Hungarian Academy of 10. Mietdnen J. Development and assessment of Sciences). Budapest 1991: 474 - 481. the SBLOCA code SMABRE. Proceedings of the Specialists Meeting on Small Break 4. Kaloinen E, Siltanen P, Terasvirta R. Two- LOCA Analyses in LWRs. University di group nodal calculations in hexagonal fuel Pisa. Vol. 2. Pisa, Italy, 1985: 481-495. assembly geometry. Proceedings of a Specialists' Meeting on The Calculation of 11. Kyrki-Rajamaki R, Raty H. User's manual 3-dimensional Rating Distributions in of the accident analysis code SMATRA. Operating reactors, Paris, November 26 - Technical Research Centre of Finland, 28, 1979. OECD, Paris, 1980: 111 - 128. Nuclear Engineering Laboratory, technical report RFD-31/92. Espoo 1992: 23 p. 5. Kaloinen E, Terasvirta R, Siltanen P. HEXBU-3D, a three-dimensional PWR- 12. Siltanen P. WER-440 core simulator test simulator program for hexagonal fuel problem on Loviisa-1 Cycles 1, 2 and 3. assemblies. Espoo 1981. Technical Research Meeting of Thematic Group 6 of the Research Centre of Finland, Nuclear Temporary International Collective (VMK) Engineering Laboratory, Research Report for Joint Research into the Physics of 7/1981: 148 p + app. 5 p. WER-type Reactors. Moscow, USSR, May 23 - 27, 1983: 5 p. + app.

IV/21 FINNISH CENTRE FOR RADIATION AND NUCLEAR SAFETY STUK-YTO-TR 69

13. P Siltanen P, Antila M. Test problem on 19. Kyrki-Rajamaki R, Miettinen J, Raty H, low leakage cores of Loviisa NPS. Meeting Vanttola T. Validation of SMATRA of Thematic Group 2 of the Temporary accident analysis code against Loviisa plant International Collective (VMK) for Joint data. "3rd International Symposium on Research into the Physics of WER-type Power Plant Transients - 1992 ASME Reactors. Rheinsberg, GDR, March 28 - Winter Annual Meeting." 8. - 13.11.1992 31, 1989: 8 p. + app. Anaheim, USA.

14. Kaloinen E, Rajamaki M. The numerical 20. CASMO-HEX is based on the well-known accuracy of the HEXBU-3D code for CASMO code of Swedish origin, see: application to the reactor core consisting of Ahlin A, Edenius M, Haggblom H. large homogeneous nodes. Presented in the CASMO, a cell and assembly spectrum 13. Symposium on WWER Physics of the code. Studsvik Energiteknik AB, VMK. Technical Research Centre of Studsvik/RF-77/6276. Nykdping 1980: lip. Finland, Nuclear Engineering Laboratory, + app. lip. Technical report REP-12/84. Curtea de Arges, Romania, 30.9. - 6.10.1984: 22 p. 21. Raty H, Kyrki-Rajamaki R, Rajamaki M. Validation of the reactor dynamics code 15. Kaloinen E. TRICON, a two-dimensional TRAB. Technical Research Centre of multigroup diffusion code for trigonal or Finland, Nuclear Engineering Laboratory, hexagonal mesh. Technical Research Centre Research Report 729. Espoo 1991: 31 p. of Finland, Reactor analysis group, Report 1. Espoo 1973: 60 p. + app. 12 p. 22. Antila M, Kyrki-Rajamaki R, Rajamaki M, Raty H, Siltanen P, Vanttola T. Application 16. Rypar V, Racek J, Fahrmann K.-H,. of the Synthesis Model in an Asymmetric Grundmann U, Ziegenbein D. Neutron Reactivity Disturbance of the WER-440 Kinetics Investigations at LR-0 Zero-Power Type Loviisa Reactors. ANS Nuclear Reactor, Nuclear Science and Engineering Reactor Safety Division International 105, 1990: 218-232. Topical Meeting: Safety of Thermal Reactors. July 21 - 25, 1991, Portland, 17. Grundmann U, Hddek J. Calculation of Oregon, USA. American Nuclear Society. Neutron Kinetic Experiments with the Code La Grange Park, USA, 1991: 261 - 268. DYN3D/M1, Kernenergie 34, 1/1991: 12- 20. 23. Kyrki-Rajamaki R. User's manual of HEXTRAN, version 1. Technical Research 18. Stenius T. Validation of the three- Centre of Finland, Nuclear Engineering dimensional reactor dynamics code Laboratory, technical report RFD-44/92. HEXTRAN against LR-0 reactor Espoo 1992: 18 p. measurements. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Technical report RFD-20/92. 38 p + app.

IV/22 The first three-dimensional dynamic AER benchmark problem is a kinetic benchmark on a control rod ejection in a VVER-440 type reactor. No thermal hydraulic feedback is included in the benchmark; the power increase is ended by reactor trip.

The reflectors and the VVER-440 control rods were described by nodes with different cross sections in the first version 1A of the benchmark problem. However, the non-multiplying reflector regions can not be modelled as ordinary nodes in HEXTRAN, because the sharp decrease of flux in reflectors can not be described properly by the present model of intrinsic nodal flux. The new nodal solution method (advanced homogenization method with discontinuity factors) tested in HEXBU-3D /8/ will make this possible. The emphasis of this paper is therefore on the second version IB of the benchmark, where albedoes can be used for reflectors and also for control rods.

The horizontal map of the reactor in half core symmetry defined in the benchmark IB is shown in Figure 1. The core consists of 3 different fuel materials. The vertical cross section of the core is in Figure 2. At the beginning of the benchmark the regulating control rod group is inserted deeply in the core. During 0.08 seconds one control rod (222 in Figure 1.) is ejected from the core. At time 1 s the reactor trip begins and all control rods including the regulating group are inserted into the core.

The two different control rod models of HEXTRAN are used in the calculations: the proper description of the large VVER-440 flux trap type control rods with albedoes at the boundaries of the absorber part and with moving fuel model of the control rod followers and the simpler control rod model with two sets of cross sections intended in HEXTRAN originally for VVER-1000 finger type control rods.

The calculations were made with half core symmetry. One node was used for every fuel assembly and 20 nodes were used axially, altogether 3680 nodes. The following time-steps were used: 5 ms until time 0.14 s, 10 ms until time 0.2 s, 20 ms until the time 2 s and 40 ms to the end of the calculation at 6 s.

HEXTRAN RESULTS

In Figure 3. the dynamic results of HEXTRAN with the two different control rod models are shown. The moving follower model gives slightly larger power peak. The difference in dynamic results is probably caused by the different stationary reactivity values of the ejected rod : moving follower model 494 pcm and cross section finger rod model 490 pcm. The albedoes and cross sections of control rods given in the benchmark problem IB were calculated to be equivalent with KIK03D code /2/. However, already minor differences of power distributions can cause these very small reactivity deviations of a few perns, which have dynamic effects in this very sensitive benchmark.

An additional curve can be seen in Figure 3. It was calculated with the cross section (finger) model and with the Stationary reactivity value of the ejected control rod modified to be the same (482 pcm) as given by KIK03D /2/. It was calculated in order to show that the differences of the dynamic results between different codes are also mainly due to differences caused by stationary reactivity worths of the ejected rod.

V/2 Reprinted with permission from the publisher. PAPER V In: Proceedings of the third Symposium of AER. Piestany, Slovakia 27 September - 1 October 1993. Budapest: KFKI Atomic Energy Research Institute, 1993. Pp. 293 - 301.

CALCULATION OF THE FIRST THREE-DIMENSIONAL HEXAGONAL DYNAMIC AER BENCHMARK PROBLEM WITH HEXTRAN

R. Kyrki-Rajamaki Technical Research Centre of Finland (VTT) Nuclear Engineering Laboratory P.O.Box 208, FIN-02151 Espoo, Finland Tel. +358 0 456 1, Fax +358 0 456 5000

ABSTRACT

Detailed results calculated with VTT’s reactor dynamics code HEXTRAN for the first dynamic AER benchmark problem are presented. They are also included in the comparison report of the benchmark. Effects of model variations on the results are presented and discussed.

HEXTRAN is a three-dimensional reactor dynamics code for VVER reactors, developed in the Technical Research Centre of Finland. It is based on the stationary code HEXBU-3D and on the one-dimensional reactor dynamics code TRAB. The thermohydraulics circuit model SMABRE has been dynamically connected to HEXTRAN for the primary and secondary loop calculations.

The first three-dimensional hexagonal dynamic AER benchmark problem is a kinetic benchmark on a control rod ejection in a VVER-440 type reactor. No thermal hydraulic feedback is included in the benchmark; the power increase is ended by reactor trip. The emphasis of this paper is on the second version IB of the benchmark, where albedoes are used for reflectors and alternatively cross sections or albedoes can be used for control rods. The two different control rod models of HEXTRAN are used in the calculations: the proper description of VVER-440 type moving control rod followers and the simpler cross section model designed for VVER-1000 finger type control rods. The dynamic results of both models are very similar.

INTRODUCTION

A three-dimensional hexagonal kinetic benchmark problem was defined in the 2nd symposium of AER in Paks 1992 /!/ and it’s results calculated with different codes including HEXTRAN are compared in another paper of this meeting /2/. In this paper results calculated with VTT’s reactor dynamics code HEXTRAN are presented. HEXTRAN /3,4/ is developed in the Technical Research Centre of Finland. It is based on the stationary code HEXBU-3D /5/ and on the one-dimensional reactor dynamics code TRAB /6/. The thermohydraulics circuit model SMABRE 111 has been dynamically connected to HEXTRAN for the primary and secondary loop calculations. In Figure 4. are the dynamic results of HEXTRAN with moving follower model, calculations made with 20 and 10 axial nodes and with time-steps of double lengths after the ejection. The use of longer time-steps has only a minor effect on the results.

The use of only 10 axial nodes causes some cusping to the curve during the reactor trip, although the different boundary conditions at different axial levels inside the neighbouring node of the control rod tip are included in the follower model. The highest power peak is cut off. The benchmark is especially sensitive to this phenomenon, because the power is exponentially growing at the time of the trip actuation. In real transients, the feedback effects have normally already suppressed the fastest power growth before the trip. In VVER-440 there is also in reality an intermediate area axially between the fuel rods and boron carbide steel, so that the control rod tip is not as sharp as in the benchmark.

In Figure 5. are the dynamic results of HEXTRAN with finger type cross section model, calculations made with 20 and 10 axial nodes. The same cusping effect of smaller amount of axial nodes can again be seen. The calculation with 10 nodes axially is also repeated without any control rod tip smoothening model, the cross sections of nodes with control rod partially inserted are simply calculated with volume weighting. This crude model badly distorts the results. In VVER-1000 calculations the control rod tip smoothening is not as necessary as in VVER-440 calculations, because the finger rods are not as effective as the removing of fuel.

The radial distributions of both the models are very near each other. The absolute axial power distributions at certain times are in Figure 6. The two different control rod models give nearly identical results except at the time of the power peak, when the absolute power level is different. At the end of the calculation (6 s) most of the control rods are inserted half way into the core and the axial power distribution is bottom peaked.

The HEXTRAN calculations were made with a HP Apollo Series 700 Model 735 workstation under UNIX-based HP-UX operating system. The dynamic simulation of the benchmark with the most accurate model of 3680 nodes took 10 minutes of central processor time when 224 time-steps were used.

CONCLUSIONS

The two different control rod models of HEXTRAN were used in the calculations: the description of VVER-440 type moving control rod followers and the cross section model designed for VVER-1000 finger type control rods. The dynamic results of both the models are very similar. It was also shown that by using reasonable large time-steps the results are converged so that shortening of time-steps does not anymore change them.

Axially 10 nodes are sufficient to describe the power increase caused by a control rod ejection. However, for proper description of these locally very heterogeneous effects of reactor trip over the whole core 20 axial nodes are needed. In reality, the negative feedback should decrease these effects.

There is a good reason in safety analyses to use conservative control rod reactivity values higher than predicted by best estimate codes, because the reactivity values are very sensitive to the nodewise power distribution. With the correct reactivity values, the dynamics is not sensitive to small errors in power distribution.

V/3 REFERENCES

A. Kereszturi, M. Telbisz, A Three-Dimensional Hexagonal Kinetic Benchmark Problem. 2nd symposium of AER (Atomic Energy Research) for Investigating Neutron Physics and Thermohydraulics Problems of Reactor Safety. Paks, Hungary, 21. - 26.9.1992. Budapest 1992. KFKI Atomic Energy Research Institute. P. 381-388.

M. Telbisz, A. Kereszturi, Results of a Three-Dimensional Hexagonal Kinetic Benchmark Problem. 3rd symposium of AER (Atomic Energy Research) for Investigating Neutron Physics and Thermohydraulics Problems of Reactor Safety. PieStany, Slovakia, 27.9 - 1.10.1993.

R. Kyrki-Rajamaki, HEXTRAN: VVER Reactor Dynamics Code for Three- Dimensional Transients. Proceedings of the 1st symposium of AER (Atomic Energy Research) for Investigating Neutron Physics and Thermohydraulics Problems of Reactor Safety. Rez near Prague, Czechoslovakia, 23. - 28.9.1991. Budapest 1991. KFKI Atomic Energy Research Institute. P. 474 - 481.

R. Kyrki-Rajamaki, Validation of the Reactor Dynamics Code HEXTRAN. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Research report YDI53/92, 20 p. To be published in STUK series (Finnish Centre for Radiation and Nuclear Safety).

E. Kaloinen, R. Terasvirta, P. Siltanen, HEXBU-3D, a three-dimensional PWR- simulator program for hexagonal fuel assemblies. Helsinki 1981. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Research Report 7/1981. P. 47- 49.

M. Rajamaki, TRAB, a transient analysis program for BWR, Part 1. Principles. Helsinki 1980. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Report 45. 101 p + app. 9 p.

J. Miettinen, Development and assessment of the SBLOCA code SMABRE. Proceedings of the Specialists Meeting on Small Break LOCA Analyses in LWRs. Pisa, Italy, 1985. Universita di Pisa. Vol. 2, pp. 481-495.

Kaloinen, Elja, Effect of Assembly Heterogeneity on the Nodal solution Method of HEXBU-3D. 1st symposium of AER (Atomic Energy Research) for Investigating Neutron Physics and Thermohydraulics Problems of Reactor Safety. 23. - 28.9.1991, Rez near Prague, Czechoslovakia. KFKI Atomic Energy Research Institute. P. 356-371. Figure 1. Horizontal map of the reactor in half core symmetry defined in the benchmark IB. Numbers 1, 2 and 3 are different fuel materials, numbers 11 and 12 are control rods participating in the reactor trip, numbers 22 and 222 are the controlling group, from which the control rod 222 is ejected.

Figure 2. Vertical cross section of the core at the beginning of the benchmark with the regulating control rod group deeply inserted.

V/5 AER Benchmark IB HEXTRAN Results with Different Models

LEGEND Follower model _ Finge r rods model Modified reactivity

CD £ O cl CD $-< O u

Time (s)

Figure 3. Dynamic results of HEXTRAN with different control rods models, and an additional curve with stationary reactivity value of the ejected control rod modified to be the same as given by KIK03D HI.

V/6 AER Benchmark IB HEXTRAN Results with Different Models

LEGEND HEXTRAN follower 20 HEXTRAN follower 20 At 2 HEXTRAN'folTowe'r' 10 -

CD £ £

Time (s)

Figure 4. Dynamic results of HEXTRAN with moving follower model, calculations made with 20 and 10 axial nodes and with time-steps of double lengths after the ejection.

V/7 AER Benchmark IB HEXTRAN Results with Different Models

LEGEND HEXTRAN finger 20 _ _ HEXTRAN.finger 10______.... HEXTRAN finger . 10 no tip Sh Q) £ %-> O O

Time (s)

Figure 5. Dynamic results of HEXTRAN with finger type cross section model, calculations made with 20 and 10 axial nodes and with 10 nodes without any control rod tip smoothening model.

V/8 AER Benchmark IB HEXTRAN Results with Different Models

at time 1 s

Absolute axial power HEXTRAN follower HEXTRAN. finger

0.08 s

0.04 s

Relative core height

Figure 6. Absolute axial power distributions of HEXTRAN at certain times with different control rods models.

V/9 Reprinted with permission from the publisher. PAPER VI In: Proceedings of the International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses. Portland, OR 30 April - 4 May 1995. La Grange Park, IL: American Nuclear Society, 1995. Pp. 274 - 283.

CALCULATION OF LOCAL BORON DILUTION ACCIDENTS WITH THE HEXTRAN CODE

Riitta Kyrki-Rajamaki and Thomas Stenius VTT Energy, Nuclear Energy P.O.Box 1604, FIN-02044 VTT, Finland Tel. +358 0 456 5015, Fax. +358 0 456 5000 E-mail: [email protected]

ABSTRACT

Possibilities of Reactivity Initiated Accidents (RLA) due to local boron dilution slugs entering the core of PWRs have been widely studied in recent years. In Finland the main analysis tool for reactor dynamics RLA calculations has been the three- dimensional HEXTRAN code which also includes full circuit models. Reliable calculation of propagating boron fronts is very difficult with standard numerical algorithms because numerical diffusion tends to smoothen the front. Thus the reactivity effect of the boron dilution can be significantly lowered and conservatism of the analyses cannot be guaranteed. In normal flow conditions this problem has been avoided in HEXTRAN analyses by simulating the dilution front directly to the core inlet. In natural circulation conditions there occurs significant numerical diffusion even during the propagation of boron front inside the core. Therefore a new hydraulics solution method PLIM (Piecewise Linear Interpolation Method) has been applied to HEXTRAN. Examples are given of analyses made with HEXTRAN in both flow conditions.

I. INTRODUCTION

Boron dilution accidents have been widely studied in recent years1, 1 \ Analyses of the possibilities and potential consequences of local boron dilution are also going on for the VVER-440 reactors in Loviisa, Finland4. Reactor dynamics calculations of local boron dilutions both in normal and in standby conditions and during accidents are being made in VTT Energy in cooperation with I VO International Ltd.

The reactor dynamics calculation system of VTT Energy consists of models for both reactor types in Finland - the ABB Atom type BWRs in Olkiluoto and the VVER type PWRs in Loviisa. HEXTRAN is a three-dimensional hexagonal transient and accident analysis code developed in VTT for VVERs, jointly funded by VTT and Finnish Centre for Radiation and Nuclear Safety (STUK). Now it is possible to make fully realistic accident analyses starting from accurate core conditions. The thermal hydraulics model SMABRE is dynamically coupled with HEXTRAN for the primary and secondary circuit calculations. In the analyses of RIAs due to boron dilution, the thermal hydraulics and reactor kinetics phenomena in the reactor core are inseparable and their iterative solution is obligatoiy.

HEXTRAN has been extensively applied to safety analyses of the Loviisa power station, the new Russian VVER-91 concept and the Hungarian VVER-440 type NPP Paks. Main applications are the calculations of asymmetric accidents in the reactor core originating from neutronic or thermal hydraulic disturbances in core or cooling circuits. HEXTRAN needs only a few seconds of CPU time for calculation of one time-step with HP’s 9000/715 UNIX workstations, so also such long accidents as Anticipated Transients Without Scram (ATWS) have been analyzed. In Chapter II the main properties of HEXTRAN are described and in Chapter III the new hydraulics solution method PLIM applied in the new version of HEXTRAN (HEXTRAN-PLIM) is presented. In Chapter IV the effects of the new solution method on the boron dilution calculations are shown in different flow conditions. An example of a HEXTRAN analysis is given in Chapter V and conclusions are drawn in Chapter Vf.

II. MODELS OF HEXTRAN

HEXTRAN5 is developed for analyses of VVER-440 and VVER-1000 reactors. It is based on the three-dimensional stationary fuel management code HEXBU-3D6 and on the one-dimensional reactor dynamics code TRAB7 . It describes accurately the WER core consisting of hexagonal fuel elements. HEXTRAN is intended for calculation of accidents, where radially asymmetric phenomena are included and both neutron dynamics and two-phase thermal hydraulics are important, e.g. control rod ejection. The thermal hydraulic circuit model SMABRE® has been dynamically coupled to HEXTRAN for analyses of accidents including effects of the whole cooling system, such as main steam line break or startup of an inoperable loop. Different connection geometries between HEXTRAN and SMABRE can be defined.

The circuit hydraulics solution consists of five conservation equations for mass and enthalpy of vapor and liquid and the momentum for the mixture. The phase separation modelling is based on the drift-flux approach. The process description is based on generalized nodes, junctions connecting nodes and heat structures describing structure walls, fuel rods and steam generator tubes. Advanced fast non-iterative numerical schemes applying sparse matrix solvers are used for the solution of discretized conservation equations.

In the core models advanced time integration methods are used. Time discretization is made by implicit methods which allow flexible choices of time-steps. In the thermal hydraulics of the core the numerical method for conservation equations can be varied between central difference and fully implicit.

The neutron kinetics model of HEXTRAN solves the two-group diffusion equations in a homogenized fuel assembly geometry by a sophisticated, fast nodal method. Within nodes the two group fluxes are represented by linear combinations of two spatial modes, the fundamental and the transient mode of solution. The dynamic equations include six groups of delayed neutrons. The feedback effects from xenon-poisoning, fuel and coolant temperatures, coolant and soluble boron densities are included in the code. A special treatment has been developed for the dynamic calculation of the moving fuel assemblies of big follower-type control elements which are used in the VVER-440 type reactors. Core symmetries for full core, half core, 1/3 or 1/6 can be used. Burnup data evaluated with HEXBU-3D can be used as such in HEXTRAN.

The thermal hydraulics in the core is calculated in separated axial hydraulic channels, which connect freely to one or several fuel assemblies. In VVER-440 type reactors there is no mixing between the hydraulic channels in the core because there are shroud tubes around individual fuel assemblies. Channel hydraulics is governed by the conservation equations for steam mass, water mass, total enthalpy and total momentum, and by appropriate correlations. The mass flow distribution between the channels is based on the pressure balance over the core. The phase velocities may be interconnected by a slip ratio or the drift-flux formalism. The properties of water and steam are represented as rational functions of pressure and enthalpy.

In order to get an accurate representation of the fuel temperature based Doppler feedback the heat transfer calculation with several radial meshes is made for an average fuel rod in each fuel assembly (divided also axially in several nodes). The release of prompt and delayed nuclear heat in fuel or in coolant is also modelled. The heat conduction equation is solved according to Fourier’s law with temperature dependent thermal properties of fuel pellet, gas gap and fuel cladding and with different heat transfer coefficients for different hydraulic regimes.

VI/2 Hot channel analysis including local fuel and cladding temperatures and cladding oxidation is also provided. The hot channel calculations are made afterwards on the basis of the output files of HEXTRAN with the one-dimensional reactor dynamics code TRAB. Sensitivity studies with different conservatisms can easily be carried out. The extreme phenomena modelled are the fuel temperature rise after occurrence of the boiling crisis and oxidation of the cladding material.

There is not very much experience in the world in making conservative safety analyses with a best-estimate three- dimensional reactor dynamics code. A new multiple hot channel methodology has been developed for this purpose.

A summary report on the validation of HEXTRAN has been published in the STUK series9. HEXTRAN is based on already validated codes and the models of these codes have been shown to function correctly also within the HEXTRAN code. The main new model of HEXTRAN, the spatial kinetics model has been successfully validated against Czech LR-0 test reactor and Loviisa plant measurements. In the stationary state the neutronic solution of HEXTRAN is the same as that of HEXBU-3D, which has been validated by thorough comparisons with Loviisa plant data.

The reactor dynamics analyses are supported by the reactor physics calculation system of VTT Energy. Reactor physics data for the dynamics codes can be generated starting from the basic nuclear data libraries, by usingVTT ’s hexagonal version of the CASMO code, CASMO-HEX. The same data can be used in HEXTRAN and HEXBU-3D.

III. THE NEW HYDRAULICS SOLUTION METHOD PLIM

A problem in computational fluid dynamics is the avoidance of typical numerical errors in solutions to the hydrodynamic flow equations. These numerical errors cause diffusion and oscillations in the most essential parts of the solution. A new shape-preserving characteristics method, Piecewise Linear Interpolation Method, PLIM10,11 has been recently developed at VTT Energy for solving one-dimensional hyperbolic equations. The basic idea of the PLIM algorithm is to form a piecewise linear approximation for every variable, containing two unknown parameters between each mesh-point in the discretized grid. The theoretical basis of the PLIM algorithm is, however, rather complex and it will therefore not be presented here. For a more detailed description of the PLIM algorithm see reference 10 or 11. Based upon the PLIM algorithm, a computational fluid dynamics code CFDPLIM has been developed. CFDPLIM has been tested in several demanding flow problems12'l3.

Conventional numerical algorithms have difficulties in simulating the transport of sharp fronts in the coolant channels, e.g. of a local boron dilution front. In the boron dilution analyses carried out with HEXTRAN the dilution slugs have been simulated directly to the core inlet in order to minimize the effect of numerical diffusion which tends to reform the boron dilution front into a ramp. However, some numerical diffusion occurs also during the propagation of the diluted slug into the core, especially if the coolant velocity is low. If the time-steps are lengthened numerical dispersion can occur. Neither dispersion nor diffusion are any problems for the PLIM algorithm, since propagating fronts can be handled properly within a mesh cell.

In reality there occurs some physical diffusion in the propagating boron front especially in large open parts of the circuit. Also the effects of turbulence can be quite strong. Hydraulics measurements on boron front propagation are either going on or in planning phase in many countries. These effects can be included in PLIM model when best estimate calculations are needed. However, inside the reactor core these mixing effects are small.

CFDPLIM has now been implemented to HEXTRAN14 and the new version of the code is here called HEXTRAN-PLIM. In the following a numerical example is given where the power of the new method can be seen. A test run for the propagation of a sharp boron front in a vertical channel simulating reactor core was carried out with the new HEXTRAN-PLIM code. The same boron dilution problem was also solved with the widely used commercial hydrodynamics

VI/3 code Phoenics version 2.0. No reactivity feedback with power effects was included in the test. The Phoenics calculations were made with two different time-steps, 0.05 and 0.005 seconds, and with two different spatial discretizations which included 10 or 100 spatial nodes. The HEXTRAN-PLIM calculation was only made with the longer time-steps (0.05 seconds) using 10 spatial nodes.

The initial concentration of boric acid was 7 g/kg (grams boric acid per kg coolant). At time 1.0 seconds the concentration at the inlet of the reactor core was changed to half of its original value i.e. 3.5 g/kg during 0.001 seconds. The concentration was then kept constant during the rest of the calculation. The velocity of the coolant in the reactor was approximately 3.55 m/s. Thus the whole boron front should propagate through the core (length 2.44 m) in 0.69 seconds preserving its original shape. The average concentrations of boron in the lowest and highest nodes were plotted as functions of time.

The solution obtained with the new HEXTRAN-PLIM code is shown in figure la. The solution is very accurate and the shape of the propagating front is preserved through the channel. No numerical dispersion or diffusion affect the solution and the minor smoothness of the solution is due to the fact that the average node values and not the calculated mesh point values of the boron concentration are shown. The use of shorter time-steps did not change the results of the HEXTRAN-PLIM code.

HEXTRAN-PLIM ------grid 1 grid 2 ------grid 3

1 . 4 1.4 Time (s) Time (s) Figure la: Boric acid concentration at the inlet and outlet of Figure lb: Boric acid concentration at the inlet and outlet of the reactor core calculated with HEXTRAN-PLIM: Az = the reactor core calculated with Phoenics. 0.244 m. At = 0.05 seconds. Equal grid 1: Az = 0.244 m, At = 0.05 s 10 times denser grid 2: Az = 0.244 m, At = 0.005 s. 100 times denser grid 3: Az = 0.0244 m. At = 0.005 s

In figure lb the results of the Phoenics calculations are shown. It can clearly be seen that numerical diffusion affects the solutions and that the error is reduced by the use of a denser grid. The obtained result was expected and very typical for any conventional numerical hydrodynamics code. The result was significantly improved when the number of mesh cells per time- step was increased to 100, but the effect of numerical diffusion was still very clear. The solution was not as good as the one obtained with HEXTRAN-PLIM, even though a 100 times denser calculation grid was used. It should be noticed that the nodes in the Phoenics calculation with grid 3 have the length 0.0244 m and thus the curve in figure lb cannot be directly compared to the HEXTRAN-PLIM curve in figure la.

It can be concluded that the PLIM algorithm is very accurate for solving problems with propagating fronts. It should be noticed that the numerical errors also affect the transport of the voids in the coolant and the enthalpy of the coolant These errors are, however, harder to detect since the void fraction and the enthalpy are changed by heat flux from the fuel rods, when the coolant moves through the flow channel.

VIM IV. EFFECTS OF THE NEW MODEL IN DIFFERENT FLOW CONDITIONS

A comparison of the HEXTRAN and HEXTRAN-PLIM codes has been carried out in different flow conditions. Two test cases of local boron dilutions in a VVER-440 reactor core were simulated. In the first simulation normal flow conditions were assumed and in the second, more challenging simulation, near natural circulation conditions were assumed in the core.

A. Test Case 1: Normal Flow Conditions

In the first test calculation a diluted slug of the volume equal to the coolant volume of the reactor core i.e. 6.7 m3 was set to move through the reactor core. The reactor was initially operating at 50 percent of its nominal thermal power (687.5 MW) and the coolant flow through the reactor core was close to nominal (7300 kg/s). The concentration of boric acid in the whole reactor was initially 7.6 g/kg, a typical value for a beginning of cycle situation. Only a reasonable mild dilution was used in the test cases in order to avoid boiling of the coolant. The calculation was made with 20 axial nodes and with only a few channels in the core. The time-step used in the calculations was 0.02 seconds.

At 1.0 seconds a slug of diluted water entered the reactor core and the boric acid concentration at the inlet decreased linearly during 0.02 seconds to a value of 7.3 g/kg. At 1.7 seconds, when the edge of the diluted slug had reached the outlet of the reactor core, the boric acid concentration at the inlet of the reactor increased linearly to its original value during 0.02 seconds.

The calculated boric acid density at the inlet of the reactor core as a function of time is shown in figure 2a. The results of HEXTRAN and HEXTRAN-PLIM are in a very good agreement with each other. Numerical diffusion does not significantly affect the results although the "comers" in the solution obtained with the HEXTRAN code are slightly rounded. The coolant density in the first calculation node remains almost constant during the transient since the increase of enthalpy in the first calculation node is insignificant compared to the inlet enthalpy of the reactor. In figure 2b the calculated boric acid density at the outlet of the reactor core is shown. There the boric acid density has significantly decreased due to the decreased density of water. The calculated results of both codes are qualitatively the same. However, both numerical diffusion and dispersion affect the solution obtained with HEXTRAN, while the HEXTRAN-PLIM solution is very stable. The original shape of the disturbance is modified by the increased power to coolant, but otherwise the shape is very well preserved. The oscillations of the boric acid density produced by the HEXTRAN code are clearly nonphysical but qualitatively the result is very close to the true solution.

6100 ------r i------1------1------i------5850 HEXTRAN-PLIM ------HEXTRAN-PLIM ------HEXTRAN ------. 5800 : HEXTRAN ------m 6050 E f Ol 5750 - ~ 6000 - >1 5700 m 5950 c 0) 5650 ^ 5900 5600 5 S85 „ 5550

S 5800 -

5750 5450 0.5 1 1.5 2 2.5 Time (s) Time (s) Figure 2a: Boric acid density at the inlet of the reactor core Figure 2b: Boric acid density at the outlet of the reactor during a boron dilution. Average flow channel, first core during a boron dilution. Average flow channel, last calculation node. calculation node.

VI/5 Generally, when purely linear numerical methods are used, numerical dispersion cannot be completely removed without an increase of numerical diffusion. The numerical algorithm used here in HEXTRAN is specially designed to minimize the total numerical error and thus both forms of numerical errors occur in the solution.

The produced fission power peaks calculated with HEXTRAN and HEXTRAN PLIM are shown in figure 3. Due to the decreased amount of boric acid in the reactor, the fission power increases and reaches a maximum value (1683 MW) at 1.68 seconds. The results of the two codes are almost identical. The local disturbances of the boric acid densities in the HEXTRAN solution do not affect the total behavior of the core.

1800 HEXTRAN-PLIM HEXTRAN 1600 -

1400 -

1200 -

1000 -

Time |s)

Figure 3: Total fission power during a boron dilution in normal flow conditions.

The calculated results of the first boron dilution test case can be considered to be in a very good agreement with each other. The HEXTRAN-PLIM code gives exactly the same universal results as the HEXTRAN code, although the numerical solution of the hydrodynamic flow produced by HEXTRAN-PLIM is more accurate and close to the ideal solution. This confirms the good performance of the HEXTRAN code under normal flow conditions.

B. Test Case 2: Natural Circulation Conditions

In the second test case of a boron dilution accident simulation, near natural circulation conditions were assumed. Thus the second case is numerically much more challenging than the first case. There are many conflicting requirements to the spatial and time discretizations and, as a consequence, the hydraulics calculational grid applied in the calculation in this test case is very far from fulfilling the Courant criterium.

The initial reactor power was 1 percent (13.75 MW) of the nominal thermal power and the mass flow through the reactor was initially 742 kg/s, which is approximately 10 percent of the nominal. The volume of the diluted slug was decreased to 50 percent of core coolant volume. The same initial and diluted boric acid concentrations as in case 1 (7.6 and 7.3 g/kg coolant) were used. The total time of the transient simulation was 20 seconds and at 1.0 seconds the diluted slug entered the reactor core. At 4.5 seconds the boric acid concentration at the inlet of the reactor was increased to its original value.

The calculated boric acid densities at the inlet of the reactor core are shown in figure 4a. The results of HEXTRAN show clear signs of numerical diffusion, while the solution obtained with HEXTRAN-PLIM is very accurate. The decrease of the boric acid density is initially faster in the solution obtained with HEXTRAN because linear approximation between the mesh points is used to calculate the node value. It can be noted that both solutions conserve very well the total mass of the boric acid which can be approximative^ seen from figure 4a using the fact that the area below the curves should be the same.

VI/6 6100 6000 HEXTRAN-PLIM — HEXTRAN-PLIM HEXTRAN — HEXTRAN 5950

6000 n 5900 5950 TJ 5850 T3 5800 5850 -

5750 5800

5750 5700 10 15 20 10 Time (s) Time (s) Figure 4a: Boric acid density at the inlet of the reactor core Figure 4b: Boric acid density at the outlet of the reactor during a boron dilution. Average flow channel, first core during a boron dilution. Average flow channel, last calculation node. calculation node.

In figure 4b the calculated boric acid densities at the outlet of the reactor core are shown. Here the HEXTRAN solution is markedly smoothened due to numerical diffusion. The HEXTRAN-PLIM solution is again nearly exact. The boric acid mass is conserved in both solutions. The most serious consequence of the smoothening of the HEXTRAN results is that the reactivity worth of the slug is decreased. Due to the finite volume of the slug, the smoothenings of the edges of the slug are combined and the maximum dilution level is not achieved at all in the upper part of the core. As expected the fission power peak produced by HEXTRAN remains clearly smaller than the peak produced by HEXTRAN-PLIM. Also the energy release is essentially smaller as can be seen in figure 5.

HEXTRAN-PLIM HEXTRAN

10 Time (s)

Figure 5: Total fission power during a boron dilution in natural circulation conditions.

In earlier analyses made with HEXTRAN in natural circulation conditions, this prominent effect on the numerical errors to simulation of finite slugs has been taken into account by using conservative assumptions. The volume of the slug has been enlarged so that the minimum concentration of boric acid has been achieved even in the last nodes at the outlet of the reactor. Using this same conservative assumption here, the power peak was 230 percent greater than the one calculated with HEXTRAN-PLIM. Increasing the volume of the diluted slug with 30 percent was enough to create a power peak in the HEXTRAN calculation as large as in the HEXTRAN-PLIM calculation with the original slug volume. Then the minimum concentration was achieved in the central part of the core but still not in the last nodes at the outlet of the reactor core. Thus the earlier mode of action in the HEXTRAN analyses has guaranteed the conservativity of the results but there has been considerable overconservatism in the analyses.

VI/7 V. EXAMPLE OF HEXTRAN ANALYSIS IN NORMAL FLOW CONDITIONS

The effects of local boron dilution both in normal and in standby conditions and during accidents are presently studied for Loviisa NPP4. Countermeasures have already been implemented in order to reduce the probability of boron dilution due to external causes. Analyses of the possibilities and consequences of inherent boron dilutions due to boiling and condensing mode during accidents are being carried out (S BLOC A, ATWS). These analyses set extreme requirements for the code. Analyses have been made e.g. in prompt recriticality conditions during shutdown when the control rods are fully inserted in the core. At the same time there can be violent boiling in the core. The coolant velocity has been varied from nominal flow to natural circulation rate.

The example of an external dilution case is an incorrect startup of an isolated loop with the other five loops operating. In VVER-440 type plants there are main gate valves in all the six primary loops. The initial power level was 13.75 MW (1 % of nominal) and the initial boric acid concentration 11 g/kg. A diluted slug of 3 m3 was assumed in the hot leg. The pump was incorrectly started before the cold leg main gate valve was opened. The diluted slug was assumed to enter only to one 1/6-sec tor of the core and mixing was conservatively assumed to happen only in the beginning of the downcomer. The water from the other loops was mixed to the diluted water until the full flow rate was achieved; the dilution was decreased from - 5 g/kg to - 4 g/kg boric acid in coolant The static overcriticality potential of the slug was 3 %.

The resulting fission power peak is about 70000 MW (figure 6a). The primary pressure increases almost to the opening level of the pressurizer safety valves, from 123 to 136 bar. Departure from nucleate boiling occurs in the hottest channels. There is some local melting in the center of fuel and the cladding temperature increases prominently over the LOCA criteria value 1200 °C. However, the maximum oxidation stays quite low (5 %) because the temperatures decrease in a few tens of seconds (figure 6b).

In figure 7 some radial distributions of the HEXTRAN results are presented. The core power distribution is strongly peaked in the diluted sector. The boiling smoothens the power distribution, but as can be seen in the figure of the fuel temperature distribution, the power integral is largest in the diluted sector.

100000 3500 LEGEND

3000 Q peliei average □ cladding outside 10000 2500

2000 1000

1000

Time (s) Time (s)

Figure 6a: Total fission power during a boron dilution Figure 6b: Fuel and cladding temperatures during a boron accident at low power level. dilution accident at low power level.

VI/8 %a) l g 1 2

Figure 7: Radial distributions in the core calculated with HEXTRAN during a local boron dilution originating from one loop: (a) fission power distribution at time of maximum power peak, relative to average power, (b) fission power distribution at time of maximum void fraction, relative to average power, (c) maximum assembly averaged fuel temperatures, (d) maximum core outlet void fractions.

If there are no closed main gate valves in the loops, there cannot exist any dilution slugs with the reactor pumps operating. A dilution slug can be formed only in situations with no forced flow. Then it enters the core at most with the speed of the first restarted reactor coolant pump or with the natural circulation flow rate which somewhat mitigates the transient. However, in the beginning of cycle the reactivity potential of pure water can be so high, especially in shutdown conditions, that if it is assumed to flow into the core without any mixing, the consequences to the fuel are not tolerable. In Finland and elsewhere there are mixing studies going on and also new measurements are being planned.

VI. CONCLUSIONS

With the HEXTRAN code reactor dynamics accident analyses such as RJA, ATWS and boron dilution analyses can be carried out. The code has been thoroughly validated and it is extensively applied for safety analyses of Loviisa VVERs in Finland. In recent years HEXTRAN and the whole VVER calculation system of VTT Energy has also been increasingly utilized for improving the safety of VVERs in Eastern Europe.

The implementation of CFDPLIM to HEXTRAN eliminates the numerical diffusion and dispersion from the thermal hydraulics solution. This application guarantees that conservative accident analysesof local boron dilutions can be done even in numerically difficult flow conditions. The comparison calculations also show the conservatism of the earlier analyses.

VI/9 REFERENCES

1 D. J. Diamond, C. J. Hsu, R. Fitzpatrick, "Reactivity accidents, a reassessment of the design-basis events". Brookhaven National Laboratory, NUREG/CR-5368 (BNL-NUEG-52198), January 1990.

2 J. Hyvarinen, "The inherent boron dilution mechanism in pressurized water reactors". Nuclear Engineering and Design vol. 145 (1993) pp 227-240.

3 S. Jacobson, "Risk evaluation of local dilution transients in a pressurized water reactor". Linkdping Studies in Science and technology, Dissertations No. 275, Linkdping University 1992.

4 M. Antila, P. Siltanen, R. Kyrki-Rajamaki, "Study of core response in reactivity accidents due to local dilution of boric acid concentration." To be published in Proceedings of the ENC ’94 ENS - ANS- FORATOM, International Nuclear Congress + World Exhibition. Lyon, France, October 2-6, 1994.

5 R. Kyrki-Rajamaki, "HEXTRAN: three-dimensional reactor dynamics code for WER-reactor cores." In Proceedings of the International Topical Meeting on Advances in Mathematics, Computations and Reactor Physics. (Pittsburgh, VA, April 4 - May 5, 1991). American Nuclear Society. LaGrange Park, 111, 30.2 4-1 - 30.2. 4-5. 1991.

6 E. Kaloinen, R. Terasvirta, P. Siltanen, "HEXBU-3D, a three-dimensional PWR-simulator program for hexagonal fuel assemblies." Research Report 7/1981. Technical Research Research Centre of Finland, Nuclear Engineering Laboratory, Helsinki, Finland, 1981.

7 M. Rajamaki, "TRAB, a transient analysis program for BWR, Part 1. Principles." Report 45. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Helsinki, Finland, 1980.

8 J. Miettinen, "Development and assessment of the SBLOCA code SMABRE." In Proceedings of the Specialists Meeting on Small Break LOCA Analyses in LWRs. Universita di Pisa, Pisa, Italy, 1985. Vol. 2, 481-495.

9 R. Kyrki-Rajamaki, "Validation of the reactor dynamics code HEXTRAN." STUK-YTO-TR 69. Helsinki, 1994. 24 p.

10 M. Rajamaki, M. Saarinen, "Accurate one-dimensional computation of frontal phenomena by PLIM." Journal of Computational Physics, Vol. Ill, No. 1 , March 1994.

11 M. Rajamaki, M. Saarinen, "PLIM shape preserving characteristics method for flow equations." In Proceedings of the International Topical Meeting on Advances in Mathematics, Computations and Reactor Physics. (Pittsburgh, VA, April 4 - May 5, 1991). American Nuclear Society. LaGrange Park, 111, 12.1 1-1 - 12.1 1-13.

12 M. Rajamaki, and M. Saarinen, "A Numerical Study of the Withdrawal and Return of Water following a Volcanic Eruption at sea." Communications in Numerical Methods in Engineering. Vol. 10. 1994.

13 M. Saarinen, "A dynamic model for low head flooding in horizontal two-phase flow." Numerical Heat Transfer, Part A, Vol. 25. 1994.

14 T. Stenius, "Implementing the characteristics-based numerical algorithm PLIM to the flow model of the reactor dynamics code HEXTRAN", MSc thesis, Helsinki University of Technology, 1994.

VI/10 Reprinted with permission from the publisher. PAPER VII In: Proceedings of the International ENS TOPical Meeting TOPFORM '95, Today's Cost Competitive NPP for Current and Future Safe Operation. Avignon, France 24 - 28 April 1995. Paris: Societe Franfaise d'Energie Nucleaire, 1995. Pp. 319 -331.

NEW SAFETY ANALYSES OF RIA AND ATWS EVENTS FOR PARS NPP

M.Telbisz, A.Gdcs, A.Kereszturi, KFKI Atomic Energy Research Institute (Hungary) P.Siltanen, IVO International Ltd (Finland) R.Kyrki-RajamSki, VTT Energy (Finland)

ABSTRACT

In Hungary an extensive work has been carried out in the AGNES project for the reevaluation of safety of the four VVER-440/213 units of NPP PARS. A set of reactivity initiated accidents with scram (RIA), and a set of anticipated transients without scram (ATWS) were calculated using the HEXTRAN and SMATRA codes. In RIA events conservative parameters were used, a single failure and an additional fault were considered in the safety system. In ATWS events best-estimate parameters were used and the failure was supposed in the scram sytem. The acceptance criteria were given on the basis of NRC and IAEA standards. In our presentation, beside the general principles and computational methods, the results of two accident analyses are illustrated. The control rod ejection accident was analyzed by IVO & VTT. The ATWS events including the inadvertent withdrawal of a control rod group were analyzed by KFKI AEKI . 1. INTRODUCTION

An extensive work has been carried out in the AGNES project (Advanced,General and New Evaluation of the Safety of Hungary ’s NPP) for the reevaluation of safety of the four VVER-440/213 units of NPP PAKS [1]. A set of reactivity initiated accidents with scram (RIA), and a set of anticipated transients without scram (ATWS) were calculated using the HEXTRAN and SMATRA codes.

The reactivity increases in RIA due to an unexpected initial event and an assumed additional fault. It leads to power rise and core damage is conceivable. A wide spectrum of RIA initial events was investigated in the project. According to the probability analysis, these events could be classified into two groups: Anticipated Operational Occurrences (AOO) and Postulated Accidents (PA).

ATWS analyses were performed in order to prove that in anticipated operational transients the reactor shut down can be achieved without scram and the acceptance limits for PA are not violated.

1.1 Acceptance criteria

The AOO has a frequency > 0.01/year. For these events the probability of heat transfer crisis is low anywhere in the core (DNB ratio is above 1.33), fuel centerline temperature and radially averaged fuel enthalpy are limited, pressures in the coolant and main steam systems are maintained below 110% of the design value. Strict dose limits are given.

VII/2 The PA has a frequency < 0.01/year. Dose limits are less strict. Cladding failures, local DNB and oxidation are allowed, but cladding temperature does not exceed 1200 °C, fuel enthalpy is below 963 J/g. Pressure limits are somewhat increased.

1.2 Events analyzed

Positive reactivity can be added to the reactor by inadvertent moving of control rods, by refuelling errors and by the decrease of moderator temperature or boron concentration. Initial events were analyzed in the following groups:

(a) Inadvertent withdrawal of control assemblies during refuelling and startup (AOO) (b) Inadvertent withdrawal of a control assembly group at different powers of reactor (AOO) (c) Control rod maloperation (AOO) (d) ' Startup of an inactive reactor coolant loop (AOO/PA) (e) Chemical and volume system malfunction (AOO) (f) Inadvertent loading and operation of a fuel assembly in an improper position (PA) (g) Control rod ejection (PA) (h) ATWS events (PA)

Every group contained several cases due to different initial assumptions. Their examinations were necessary in order to select the most serious case.

1.3 Conservative assumptions in RIA calculations

The assumptions for initial states and protection were conservative for the given transient, in order to overestimate the severity of the accident and in order to make the analysis valid for different refuelling schemes.

An overall study of the different initial states was performed for control rod initiated transients (b and g). Different initial events were investigated in group (d), the starting of a loop with incorrect temperature as well as the starting of a loop with incorrect boron concentration.

A single failure was assumed in each calculation in the most effective safety system with the most serious consequences. Other additional faults

VI1/3 and operator errors could be also assumed in a conservative manner. The generally used assumptions for reactor protection were as follows: . highest level emergency reactor protection ERP-1 was operating (with one rod stuck at scram), but lower level ERPs were not considered, . ERP-1 signal due to reactor period < 10s - was missing, . ERP-1 signal due to power level > 110% of initial power - was normally operating in full power cases, but it was retarded in cases of lower power (it was set to 110% of the nominal power as an operator error). . operator is assumed to start action only after 30 minutes, but then in the most reasonable way.

1.4 Assumptions in ATWS calculations

Best-estimate assumptions were used. The same pessimistic initial state was used in each case, it was the full power state at the beginning of cycle. Several initial events were investigated with different failures in the reactor protection system. Operator actions were assumed only after 30 minutes. 2. DESCRIPTION OF THE CODES

The reactor dynamics codes HEXTRAN and SMATRA were developed in VTT Energy for VVER analyses. The 3-dimensional code HEXTRAN [2] accurately describes the VVER core consisting of hexagonal fuel assemblies. Main applications of HEXTRAN are analyses of asymmetric accidents in the reactor core originating from neutronic or thermal hydraulic disturbances in the core or the cooling circuits. The axially one ­ dimensional code SMATRA [3] is intended for applications, where the main spatial effects occur in axial direction, e.g. ATWS. Both codes include the thermal hydraulic circuit model SMABRE [4] for the primary and secondary circuit calculations. In the core models only spatial neutronics are different.

The circuit hydraulics solution of SMABRE consists of five conservation equations for mass and enthalpy of vapour and liquid and the momentum for the mixture. The phase separation modelling is based on drift-flux approach. The process description is based on generalized nodes, junctions connecting nodes and heat structures describing structure walls, fuel rods and steam generator tubes. Fast non-iterative numerical schemes applying sparse matrix solvers are used for the solution of discretized equations.

VII/4 In the core models advanced time integration methods are used. Time discretization is made by implicit methods which allow flexible choices of time-steps. In thermohydraulics of the core the central difference and fully implicit methods can be used alternately.

The neutron kinetics model of HEXTRAN solves the two-group diffusion equations for homogenized fuel assemblies by a sophisticated nodal method. Within nodes the two group fluxes are represented by the linear combinations of two spatial modes, the fundamental and the transient mode of solution. The dynamic equations include six groups of delayed neutrons. The feedback effects from xenon-poisoning, fuel temperature, moderator density and temperature and soluble boron density are included in the program. A special treatment has been developed for the dynamic calculation of the moving fuel assemblies of follower-type control elements which are used in the VVER-440 type reactors. Core symmetries for full core, 1/2, 1/3 or 1/6 core can be used.

Thermal hydraulics in the core is calculated in separated axial hydraulic channels connecting freely to one or several fuel assemblies. In VVER-440 type reactors there is no mixing between the hydraulic channels in the core because of the shroud tubes around fuel assemblies. The distribution of mass flow between the channels is based on the pressure balance over the core. The phase velocities may be interconnected by a slip ratio or by the drift-flux formalism.

In order to get accurate Doppler feedback, the heat transfer calculation is made in each node of fuel assembly with several radial mesh points for an average fuel rod. The release of prompt and delayed nuclear heat in fuel or in coolant is modelled. The heat conduction equation is solved according to Fourier ’s law with temperature dependent thermal properties of fuel pellet, gas gap and fuel cladding and with different heat transfer coefficients for different hydraulic regimes.

The SMATRA core dynamics model includes one-dimensional models for neutronics, rod heat transfer, and thermal hydraulics, using at most three parallel axial channels. A synthesis model can be employed in neutron kinetics. It is composed of a time-dependent axial two group diffusion equation and of a radial shape function equation. The fuel temperature rise after occurrence of the boiling crisis and oxidation of the cladding material are modelled as extreme phenomena. The core model of SMATRA is used

VII/5 separately for hot channel analyses on the basis of the output tiles of the main calculations made with HEXTRAN or SMATRA.

The codes were thoroughly verified [5,6,7], The methods for generating reactor physics data, and the steady state results of the reactor dynamics codes have been verified by comparisons with plant data. Validation of the dynamics consists of calculation of start-up experiments and real plant transients, of international benchmark problems and code comparisons. The three-dimensional kinetics model of HEXTRAN has been validated by simulations of the spatial kinetics measurements on the Czech LR-0 test reactor. Thermal hydraulic circuit models have been validated with calculating eg. international standard problems. Real plant transients have been simulated both with BWR and VVER models with good accuracy.

3. CONTROL ROD EJECTION

3.1 Analyzed cases

Six different initial conditions were analyzed for control rod ejection:

(a) Full power at BOC, regulating group height 125 cm (b) Full power at EOC, regulating group height 125 cm (c) Low power at BOC, regulating group height 50 cm (d) Low power at EOC, regulating group height 50 cm (e) Low power at EOC, 3 operating RCPs, regulating group height 50 cm (f) 70% power at EOC, 5 operating RCPs, one dropped control rod in the core, regulating group height 100 cm.

The regulating group was always at the minimum height allowed by plant operational limits,250cm representing the fully withdrawn position. An off- center control assembly was ejected in every case. The ejection time was 0.2-0.3 seconds, it was determined by a constant acceleration 50 m/s2.

The analyses were performed by IVO and VTT using the HEXTRAN code with a full three-dimensional core neutronics model.

3.2 Conservative assumptions of neutronics

Although HEXTRAN is a best-estimate code, several conservative features were introduced into the initial core state by adjusting the nuclear data

VII/6 generated mainly by the code CASMO-HEX. These adjustments were made to achieve a desired limiting value or relative change in key core characteristics for certain reference states, such as full power or hot zero power with the regulating group raised to the highest allowed position 225 cm. The main conservative adjustments were the following:

The axial power distribution was adjusted to a limiting top peaked distribution at full power by an additional axial profiling of neutron production. The coolant temperature (density) coefficient for the whole core was adjusted to a desired more positive value by an additional linear dependence of neutron production on coolant density and/or increase of boron concentration in the coolant. The fuel temperature coefficient for the whole core was adjusted to be less negative by an additional linear dependence of neutron production on the square root of the absolute fuel temperature. The effective fraction of delayed neutrons was somewhat reduced. The reactivity worth of the control rods was increased by adjusting uniformly the boundary conditions for all control rods.

In particular, the calculated reactivity worth of the regulating group was increased by 25 %. This resulted in an increase of the ejected rod worth by 45 %. During reactor scram one control assembly next to the ejected one was assumed to remain stuck out of the core.

3.3 Hot channel analysis

A multiple hot channel analysis was performed in each case covering representative core locations with differing time histories of average rod power in the fuel assembly. At each location a constant excess radial peaking factor is applied to generate a hot fuel rod. The maximum value for this excess factor is determined so that it produces the maximum permissible rod peaking either in the actual initial state or in the reference full power state, whichever is more limiting. Rather than a real rod of the specific core, this represents a potential hot fuel rod at the given location. Consequences for fuel rods of lower power were then studied by reducing the excess peaking and repeating the hot channel simulation over time.

Temperature dependent over-estimate values were used for the heat conductance of the gas gap in the hot fuel rod in order to enhance the

VII/7 appearance of DNB. Consistently, this reduced the initial fuel pellet temperatures somewhat.

3.4 Results of HEXTRAN calculations

The reactivity worth of an ejected control rod tends to be higher at EOC than at BOC in absolute terms and particularly when measured in dollars. This is due to a smaller fraction of delayed neutrons at EOC. In these analyses the maximum worth of ejected rod is slightly under 1 $ at full power and about 1.8 $ at low power.

From full power a rapid excursion of the fission power up to 550 % of nominal is calculated, while the maximum power transferred to coolant reaches only 132 %. In core locations close to the ejected rod DNB is predicted for the potential hot fuel rod. The maximum fuel pellet average enthalpy reaches 310 J/g and there is a wide margin to fuel centerline melting. Cladding temperatures up to 715 °C are predicted. The most adverse conditions are calculated for the follower assembly of the ejected control rod, but nearly equal conditions can be encountered nearby. The highest fuel enthalpy 325 J/g was calculated for the case of 70 % initial power and a tilted power distribution.

From low power a prompt supercritical excursion of the fission power up to 3500 % of nominal occurs. However,the maximum power transferred to coolant reaches only 85 % in a burst of radiation and 60 % by thermal conduction. There is no DNB in the potential hot fuel rod if all six RCPs are operating. With only three pumps in operation DNB is predicted for core locations close to the ejected rod. In both cases the fuel pellet average enthalpy almost reaches 310 J/g. With DNB cladding temperatures up to 770 °C are predicted. Now the most adverse conditions are calculated for core locations next to the ejected control rod.

The pressure rise in the primary circuit assuming a minor leak is only 1 to 4 bar depending on the case.

In all cases it must be assumed that at least 126 fuel rods in the follower assembly of the ejected control rod fail due to mechanical impact.

VII/8 Figure 1. Normalized, distribution of fission power in fuel assemblies at time of power maximum in CRE from low power (Case d).

Figure 2. Distribution of average fuel temperatures in assemblies at time of maximum temperature for CRE from low power (Case d).

VII/9 4.ATVVS ANALYSES

4.1 Initial events and assumptions

Initial events leading to a defect in secondary or primary cooling were selected. Five transients were investigated:

(a) Inadvertent withdrawal of a control group (b) Loss of normal feedwater flow (c) Turbine trip (d) Inadvertent closure of the main steam isolation valves (e) Coincident loss of onsite and external a.c.power

The analyses were performed by KFKI AEKI using the SMATRA code. Best-estimate values of neutronphysical and thermohydraulical input parameters were used. The hot channel power peaking factor was limited by the operational limit for maximum linear heat rate in the initial state.

A mechanical failure was assumed in cases (b,c,d,e), whereby all absorber assemblies became unmovable. Neither ERP-1 nor lower level ERPs could move them. Other protections due to ERP-1 signal were available: automatic boration with 7s delay, turbine trip with 10s delay.

In case (a), instead of mechanical error, a common electric failure was supposed in the ERP system, which stopped all level ERP signals .

4.2 Results of SMATRA calculations

The transients were followed by the SMATRA code to 30 or 45 minutes in order to demonstrate that the shutdown of reactor could be achieved. In most cases the final shutdown could be performed by the operator only after 30 minutes when pressure became low enough to start boration. PA acceptance criteria were fulfilled in each case. Fuel temperature and enthalpy were even below A00 limits.

In the last four cases the turbines were tripped, power decreased rapidly due to moderator temperature feedback and DNB ratio was far from boiling crisis. The core at this low power was coolable until 30 minutes even in cases when the steam generators (SGs) were almost drying out.

VII/10 After boration the residual heat could be removed by emergency feedwater and by desalinated water supply to the feedwater tank.

The most serious case was the inadvertent withdrawal of a control group, due to the added reactivity, and to the missing ERP-1 signal. DNB ratio was at the limit of boiling crisis.

4.3 The inadvertent withdrawal of a control group (case a)

Turbine trip and automatic boration were not actuated because ERP-1 signal could not appear due to an electric failure.

The total reactivity value of the withdrawn control group was 3.3S, initially the rods were half-inserted, the velocity of withdrawal was 2cm/s. After finishing the withdrawal, the power reached 2430 MW (177%). As turbines were operating, the power did not sink to a low level as in other ATWS cases. Power was somewhat reduced by the increasing of the moderator temperature due to the decreasing water level in SGs but after 8 minutes it became stable at 110% of the nominal value. The DNB ratio in the hot channel was just at the critical limit of 1.33 during 3 minutes, but boiling crisis did not start. So the results seemed to be acceptable even as AOO but it was obvious that conservative parameters instead of best- estimate ones could cause some heat transfer crisis.

The increasing moderator temperature led to high primary pressure, which opened the pressurizer relief and safety valves several times. Pressure was stabilized at a rather high value, just below the setpoint of the safety valve. After stabilization only the relief valve was opened and there was a negligible water flow through it, because of the filled pressurizer. The high pressure did not allow the operator to start boration even after 30 minutes. He had the possibility to reduce power in an other way: by disconnecting electric supply of control rod drives. In this case rods dropped into the reactor and the transient finished with shut down.

The secondary pressure was not as high as in other ATWS cases, turbine bypass valves (BRU-K) were open only for a few minutes. SG’s water level decreased rapidly at the beginning due to the increased steam generation, and the auxiliary and emergency feedwaters were started. After 8 minutes the level stabilized at about 1 m.

VII/11 TOTAL FISSION POWER 2600.00

2000-

1300.00 500 1000 X: 0.20000000 Y: 1374.92320 time(s) (LIN) REACTIVITY

time(s) (LIN) MEAN WATER TEMPERATURE

time(s) (LIN) SYSTEM PRESSURE

time(s) (LIN) SO WATER LEUEL

time(s) (LIN) MAXIMUM OF DNB RATIO in hot channel

time(s) (LIN) Figure 3. Behaviour of main reactor parameters in ATWS case during the first 30 minutes of the transient ”Inadvertent withdrawal of a control group " (Case a)

VII/12 5. CONCLUSIONS

Acceptance criteria were fulfilled in all analyzed cases. Postulated accident criteria were fulfilled in conservative control rod ejection (CRE) and in best-estimate ATWS calculations. Some cladding failures occurred in CRE but they were acceptable. In ATWS the pressure values were rather high but acceptable, the safety valves were able to control them, heat transfer crisis and cladding failure did not occur. In ATWS cases the water level in steam generators decreased or even the SGs were dried out. It could be prevented by tripping of reactor coolant pumps, but in that case core cooling would be worse. In our analyses there was no RCP trip due to the plant protection signals in PAKS NPP.

ATWS analyses proved that shutdown of VVER-440 units of PAKS NPP was possible without scram in all cases.

REFERENCES

[1] AGNES PROJECT, EXECUTIVE SUMMARY, October 1994 [2] Kyrki-Rajamaki, Riitta, HEXTRAN: Three-Dimensional Reactor Dynamics Code for VVER-Reactor Cores. Proc. of the Int. Topical Meeting on Advances in Mathematics, Computations and Reactor Physics. Pittsburgh, USA, 1991, P. 30.2 4-1 - 30.2. 4-5. [3] Rajamaki, Markku, TRAB, a transient analysis program for BWR, Part 1. Helsinki 1980. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Report 45. 101 p + app. 9 p. [4] Miettinen, Jaakko, Development and assessment of the SBLOCA code SMABRE. Proc. of Specialists Meeting on Small Break LOCA Analyses in LWRs, Pisa, Italy, June 23-27, 1985, pp. 481-495. [5] Kyrki-Rajamaki, R., Validation of the Reactor Dynamics Code HEXTRAN. Helsinki 1994. Finnish Centre for Radiation and Nuclear Safety (STUK), STUK-YTO-TR 69. 24 p. [6] Raty, H., Kyrki-Rajamaki, R. & Rajamaki, M., Validation of the reactor dynamics code TRAB. Helsinki 1991. Technical Research Centre of Finland, Nuclear Engineering Laboratory, Research Reports 729. 31 p. [7] Vanttola, T., Studies on the assessment and validation of reactor dynamics models used in Finland. Espoo 1993. Technical Research Centre of Finland, Publications 156. 52 p. + app. 130 p.

VII/13 Reprinted with permission from the publisher. PAPER VIII In: ENC '94 International Nuclear Congress - Atoms for Energy. Lyon 2-6 October 1994. Berne: European Nuclear Society (ENS), 1994. Transactions. Vol.II. Pp. 105-111.

STUDY OF CORE RESPONSE IN REACTIVITY ACCIDENTS DUE TO LOCAL DILUTION OF BORIC ACID CONCENTRATION

Martti Antila, Pertti Siltanen (IVO International Ltd, Vantaa, Finland) Riitta Kyrki-Rajamaki (VTT Energy, Espoo, Finland)

1 INTRODUCTION

Recently, major attention has been given to analyzing the possibilities and potential consequences of a slug of diluted water entering the core /1,2/. Similar analyses are going on for the WER-440 reactors in Loviisa. Suitable countermeasures have already been implemented to reduce the probability of external inhomogeneous dilution. The possibility and consequences of inherent boron dilution mechanisms /3/ during Small Break Loss of Coolant Accidents (SBLOCA), Steam Generator Tube Ruptures (SGTR) and Anticipated Transients Without Scram (ATWS) are being analyzed. Inhomogeneous dilution scenarios with their high reactivity disturbance potential were not included in the original safety analyses, which are now being updated.

In this paper typical dilution scenarios are discussed. Results of potential consequences in the core for two typical external dilution scenarios according to our detailed 3-dimensional dynamics calculations are presented and the principles of the new preventive automation recently implemented at Loviisa NPS is described.

2 TYPICAL DILUTION SCENARIOS IN HOT CONDITIONS

2.1 Closing of a main gate valve

The reactor is assumed to be close to criticality during start-up dilution or to be operating at partial power. The control rods are withdrawn from the core. Reactor trip does not occur when at most three reactor coolant pumps are not in operation. The main gate valve in the cold leg of a loop may be temporarily closed due to failure of an anti-rotation device or maintenance work on the pump motor. The coolant in the loop can become stagnant. Simultaneously, the make-up water lines into the loop may be open. The full injection capacity has a potential for some of the dilution water to enter the hot leg of the closed loop. It is also conceivable that pure condensate left in the injection pipelines during preceding dilution could enter the loop. The slug of diluted water could be transported to the core if the reactor coolant pump is started before opening the main gate valve. The probability of this transient scenario was estimated to be < 3E-7/y taking into account the new preventive automation. 2.2 Stopping of all reactor coolant pumps during start-up dilution

The reactor is assumed to be close to criticality during start-up dilution or to be operating at power when all the reactor coolant pumps stop. Reactor trip is activated and the reactor becomes subcritical with inserted control rods. Natural circulation with all main gate valves open takes over. Particularly during start­ up after refuelling or after a longer outage the decay heat power of the core is small. Flow stagnation may occur in some loops. Dilution of the primary circuit after the pumps have come to a stand-still may create a slug of diluted water in one or more of the loops with open injection lines. Pure condensate or diluted water left in the injection pipelines during preceding dilution may also be pushed into the loops by continued make-up water supply. A slug of diluted water in a loop can later be transported to the core if the pump in this loop is the first one to be started. It is conceivable that restart of natural circulation could also transport the slug into the reactor. This can occur without considerable mixing only if the slug is relatively isothermal with the rest of the water in the loop. In this case the slug might reach the reactor vessel before the restart of any coolant pumps. The probability of this scenario was estimated to be < 5E-7/y taking into account the new preventive automation.

2.3 Accident conditions

In SBLOCA and ATWS events the inherent formation of a diluted slug in the loop seals is possible by a boiler/condenser cooling mode if the primary circuit coolant inventory is reduced sufficiently to stop the two phase natural circulation. During SGTR accident diluted water might flow to the primary circuit from the secondary side of the damaged steam generator. The slug can later enter the core as a result of restart of natural circulation or a reactor coolant pump /3/.

3 POTENTIAL CONSEQUENCES IN THE CORE

Even as little as 0,5 m3 of pure condensate injected into the hot leg at the beginning of cycle has the potential for a severe reactivity accident in an operating reactor if it entered the core with minimal mixing as a diluted slug filling one sixth of the core at the flow velocity of operating pumps.

Two reactivity values of potential core disturbances are of interest, the criticality limit (ke££ = l) and the reactivity initiated accident (RIA) limit kRIA , beyond which the hottest fuel rods may already disintegrate. From basic reasoning applying the Fuchs-Hansen model for rapid power excursions this limit is estimated to be at least kRIA=1.025 for fast reactivity insertions (< 1 second) . The effects of power peaking are included in this estimate. With slow reactivity insertion rates the consequences become milder. The static kRIA serves as a conservative screening limit for severe reactivity accidents in

VIII/2 WERs. The core design code HEXBU-3D /4/ was used to study the static reactivity effects of diluted slugs of different geometries in the core. Different reactor states, either critical or shut down with control rods were analyzed.

The estimated RIA limit of reactivity was confirmed with the reactor dynamics code HEXTRAN /5/. HEXTRAN is a three-dimensional reactor core dynamics code for coupled neutron kinetic and thermalhydraulic calculation of WER type reactors. Hot channel analysis capability including local fuel and cladding temperatures and cladding oxidation is also provided. HEXTRAN is dynamically coupled with the code SMABRE /6/, which is a thermal- hydraulic model of the primary and secondary circuits. The coupled code was used in the analyses.

It is well known that numerical diffusion tends to destroy the sharp boron fronts in codes which use the standard solution methods. This problem was avoided by simulating the dilution front directly to the core inlet of HEXTRAN as external time- dependent input. The timing, duration and volumes were evaluated from the prerun of SMABRE alone. The flow velocity and assumed mixing are of great importance. The results for the two events described above are summarized below.

3.1 Incorrect start-up of an isolated loop

The first case is the incorrect start-up of an isolated loop when the other five loops are operating and the reactor power is 1 %. In the analysis a diluted slug of 3 m3 was assumed in the hot leg. The pump was started and then the cold leg main gate valve was opened. A diluted slug originating in the hot leg enters the reactor vessel with the highest flow rate and subsequently enters the core with the highest volume fraction. From steady state experiments at the plant it is known that the coolant pumps feed essentially their own sectors in the core with limited mixing with water from other loops. Some mixing of the dilution front occurs in the steam generator due to flow pathways of different length. These mixing effects were not taken into account in the base case. It was assumed that the flow from the accelerating loop comes to its own sector, where it mixes with the water from the other loops until full flow rate for the starting loop is reached. In the base case the original dilution in the hot leg was -913 ppm, which is reduced to -730 ppm in the core due to lower flow rate in the starting loop. This disturbance produces the static multiplication factor ke££=l. 030 when the slug fills a 60° sector of the core. The core power distribution is strongly peaked in the disturbed sector.

The hot fuel pellet temperature and the hot spot cladding outside temperature as a function of time are given in Fig. 1. The maximum fuel pellet average enthalpy is 960 J/gU02. A fuel centerline temperature exceeding 2800 °C is not physical and represents fuel enthalpy beyond the melting point of U02. Maximum cladding temperature was 1660 °C and cladding oxidation 5 %. Primary circuit peak pressure was 13 5 bar, which is just below the safety valve opening pressure 137 bar.

VIII/3 3500-1 3500

P« 3000- 3000- W 3000

2500- W 2500

M 2000- W 2000- Q 2000

1500- 1500- 1500

1000- 1000- 1000

500-

0 S 10 15 20 25 30 35 40 45 50 TIME (S)

Figure 1. Maximal temperatures of fuel center, pellet average and cladding outside as a function of time in case 3.1.

The acceptance criterion of the Finnish safety authority for pure RIA events is the fuel pellet average enthalpy limit 963 J/gU02 (230 cal/gU02) . This limit is almost reached, which implies that the assumed disturbance is essentially at the limit for severe core damage. As can be seen from Fig. 1 the LOCA limit 1200 °C for the cladding temperature is exceeded for a short time but the cladding oxidation is well below the limit of 17 %.

3.2 Restart of the first reactor coolant pump

The second case is the restart of the first coolant pump after stop of all pumps. The reactor is subcritical with all the control rods in the core. It is assumed that diluted water has been accumulated in one loop (16 m3) due to continued dilution and stagnant coolant conditions in the primary circuit. In the base case a whole core disturbance -1286 ppm corresponding to the static ke££=l .025 for the shut down core was calculated. This is equivalent to injecting the minimum allowed boron concentration and assuming a temperature difference of -30 °C. The disturbance enters the whole transverse area of the core at the flow velocity of one coolant pump.

The hot fuel pellet temperature and the hot spot cladding outside temperature as a function of time are given in Fig. 2. The peak fuel pellet enthalpy was now only 390 J/gU02. Maximum cladding temperature was, however, 1100 °C because of DNB and the conservatively long duration of the disturbance. Cladding

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The mixing of pure condensate with the recirculation flow in the coolant purification system is at the moment ensured by limiting the flow rate of pure condensate and by monitoring the mixing condition with the process computer system. This is to ensure, that the boron concentration in the pipelines of the make-up water system is not lower than what is acceptable according to the reactivity accident analyses. In the future a separate tank will be installed, from which the dilution water of specified boron concentration is taken to the present degasifier of pure condensate to ensure that the dilution limit is not exceeded in any case.

The flushing of closed loops by reverse flow is enforced by new automation that requires the main gate valves to be fully open before a pump can be started. The automation includes an intermediate partial opening of the valve for 400 seconds to limit the initial flushing rate.

When all the reactor coolant pumps have stopped, the first pump to be restarted shall be selected from a loop with no makeup water injection.

5 CONCLUSIONS

New preventive automation and operating procedures have been implemented at Loviisa NPS to reduce the probability and consequences of external boron dilution in hot conditions. Detailed 3-dimensional reactor core dynamic calculations were performed to confirm the allowable minimum boron concentration for the dilution water. It was found that the RIA limit for the static multiplication factor of the disturbed core is kRIA > 1.025. The lower limit applies to fast reactivity insertions with essentially fuel temperature feedback only. It is clearly beyond mere prompt criticality. At reduced coolant flow rates there is additional margin due to the slower reactivity insertion rate in itself and due to reactivity feedback from coolant density. The degree of inherent protection provided by coolant mixing phenomena in the steam generators, loop piping and reactor vessel requires further study.

6 REFERENCES

/!/ D.J. Diamond, C.J. Hsu, R. Fiztpatrick: Reactivity Accidents, A reassessment of the Design-Basis Events. Brookhaven National Laboratory, NUREG/CR-5368 (BNL-NUREG-52198), Jan. 1990.

Ill S. Jacobson: Risk Evaluation of Local Dilution Transients in a Pressurized Water Reactor. Lindkdping University, Studies in Science and Techno1., Dissertations No. 275,1992.

VIII/6 /3/ J. Hyvarinert: An Inherent Boron Dilution Mechanism in Pressurized Water Reactors. Fifth Topical Mtg. on Reactor Thermal Hydraulics (NURETH-5), Salt Lake City, Sept. 1992.

/4/ E. Kaloinen, P. Siltanen, R. Terasvirta: Two-group Nodal Calculations in Hexagonal Fuel Assembly Geometry.OECD/ NEA Specialists' Mtg. on the Calculation of 3-Dimensional Rating Distributions in Operating Reactors, Paris, Nov. 26-28, 1979, pp. 111-128.

/5/ R. Kyrki-Rajamaki: HEXTRAN: Three-Dimensional Reactor Dynamics Code for WER-Reactor Cores. ANS Topical Mtg. on Advances in Mathematics, Computations and Reactor Physics. Pittsburgh, USA, 28.4-2.5.1991.

/6/ J. Miettinen: Development and Assessment of the SBLOCA Code SMABRE. Proceedings of the Specialists Meeting on Small Break LOCA Analyses in LWRs. Pisa, Italy, 1985.

VIII/7 Published by Series title, number and report code of publication Vuorimiehentie 5, P.O.Box 2000, FIN-02044 VTT, Finland VTT Publications 246 VTT-PUBS-246 Phone intemat. + 358 0 4561 Telefax + 358 0 456 4374 Date Project number October 1995 Author(s) Name of project Kyrki-Rajamaki, Riitta

Commissioned by

Title Three-dimensional reactor dynamics code for VVER type nuclear reactors

Abstract A three-dimensional reactor dynamics computer code has been developed, validated and applied for transient and accident analyses of VVER type nuclear reactors. This code, HEXTRAN, is a part of the reactor physics and dynamics calculation system of the Technical Research Centre of Finland, VTT. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and the two-phase flow equations of hydraulics. It includes all the experience of VTT from 20 years on the accurate three-dimensional static reactor physics as well as on the one-dimensional reactor dynamics. The dynamic coupling with the thermal hydraulic system code SMABRE also allows the VVER circuit-modelling experience to be included in the analyses. With HEXTRAN it is possible to make realistic time-dependent analyses starting from the actual core cycle conditions. Methods for making conservative accident analyses with this best-estimate code have also been developed. The usefulness of the three-dimensionality is shown particularly in accidents with asymmetric fission power distribution originating from local neutronic or thermal hydraulic disturbances in the core or cooling circuits. Complicated accidents in which there are strong interactions between neutron kinetics and thermal hydraulics can be reliably analyzed. The new hydraulics solution method PLIM developed at VTT has been applied in HEXTRAN to remove modelling restrictions and to eliminate numerical diffusion and dispersion. The use of PLIM improves accuracy and expands the applicability range of the code. HEXTRAN has been validated against different types of relevant information available, viz. measurements of a test reactor, start-up experiment and other data of a real plant, as well as with calculations of several international benchmark problems and independent code comparisons. HEXTRAN’s applicability to calculate VVER-440 and VVER-1000 type reactors has been demonstrated. Extensive analyses have been carried out with HEXTRAN on both design basis and new types of accidents, e.g. RIA, ATWS or local boron dilutions, for the Finnish Loviisa and Hungarian Paks nuclear power plants as well as for the new Russian VVER-91 concept.

Activity unit VTT Energy, Nuclear Energy, Tekniikantie 4 C, P.O.Box 1604, FIN-02044 VTT, Finland ISSN and series title 1235-0621 VTT PUBLICATIONS ISBN Language 951-38-4784-5 English Class (UDC) Keywords 621.039:681.3:621.039.4 nuclear reactors, reactor dynamics, three-dimensional kinetics, HEXTRAN, mathematical models, computer programs, validation, accident analysis, WWER type reactors, hexagonal friel

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224 Leinonen, Heikki. Evaluation of stress corrosion cracking susceptibility of austenitic stainless steels in CaCl2 solution by the constant load method. 1995. 53 p. 225 Koljonen, Tatu. Simulation of the mashing process. 1995. 138 p. + app. 7 p. 226 Kokko, Erkki & Fan, Youchen. Ageing of cellular plastic insulations. 1995. 90 p. 227 Leppala, Kari. Inside a contract research laboratory. A study of concepts, methods and performance. 1995. 250 p. + app. 22 p. 228 Pajari, Matti. Shear resistance of prestressed hollow core slabs on flexible supports. 1995. 132 p. 229 Smolander, Maria. Electrochemical aldose detection with PQQ-dependent aldose dehydrogenase. 1995. 60 p. + app. 44 p. 230 Isomursu, Pekka. A software engineering approach to the development of fuzzy control systems. 1995. 79 p. + app. 55 p. 231 Hanhijarvi, Antti. Modelling of creep deformation mechanisms in wood. 1995. 143 p. + app. 3 p. 232 Laukkanen, Marja-Leena. Single-chain antibodies. Bacterial production, bio ­ synthetic lipid tagging and use in the preparation of immunoliposomes. 1995. 84 p. + app. 25 p. 233 Kulmala, Risto. Safety at rural three- and four-arm junctions. Development and application of accident prediction models. 1995. 104 p. + app. 42 p. 234 Mustranta, Annikka. Novel applications of lipases. 1995. 83 p. + app. 48 p. 235 Hasemann, Jorg-Michael. Planning and monitoring in dynamic environments. 1995. 101 p. 236 Jokela, Timo. Modeling the external behavior of electronic products. 1995. 47 p. 237 Lanu, Matti. Testing fibre-reinforced concrete in some structural applications. 1995. 67 p. + app. 4 p. 238 Sarja, Asko & Hannus, Matti. Modular systematics for the industrialized building. 1995. 216 p. 239 Marquis, Gary & Kahonen, Asko. Fatigue testing and analysis using the hot spot method. 1995. 35 p. + app. 2 p. 240 Marquis, Gary B. High cycle spectrum fatigue of welded components. 1995. 83 p. + app. 100 p. 241 Savola, Reijo. A state space generation tool for LOTOS specifications. 1995. 99 p. + app. 6 p. 242 Tenkanen, Maija. Characterization of esterases acting on hemicelluloses. 1995. 94 p. + app. 59 p. 243 Laitinen, Kari. Natural naming in software development and maintenance. 1995. 99 p. + app. 70 p. 244 Vesterinen, Raili. Gasification of waste preserved wood impregnated with toxic inorganic and/or organic chemicals. Gasification tests with impregnated waste wood at the 5 MW Jalasjarvi gasification plant. 1995. 38 p. + app. 35 p. 246 Kyrki-Rajamaki, Riitta. Three-dimensional reactor dynamics code for VVER type nuclear reactors. 1995. 51 p. + app. 80 p. 248 Suoranta, Risto. Amplitude domain approach to digital filtering. Theory and applications of L-filters. 1995. 199 p. ISBN 951-38 —4784-5 ISSN 1235-0621 Copyright © Valtion teknillinen tutkimuskeskus (VTT) 1995

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VTT Energia, Ydinenergia, Tekniikantie 4 C, PL 1604, 02044 VTT puh. vaihde (90) 4561, telekopio (90) 456 5000 VTT Energi, Kamkraft, Teknikvagen 4 C, PB 1604, 02044 VTT tel. vaxel (90) 4561, telefax (90) 456 5000 VTT Energy, Nuclear Energy, Tekniikantie 4 C, P.O.Box 1604, FIN-02044 VTT, Finland phone intemat. + 358 0 4561, telefax + 358 0 456 5000

Technical editing Leena Ukskoski

VTT OFFSETPAINO, ESPOO 1995 A three-dimensional reactor dynamics computer code HEXTRAN has been developed, thoroughly validated, and extensively applied for transient and accident analyses of VVER type nuclear reactors. HEXTRAN models accurately the VVER core with hexagonal fuel assemblies. The code uses advanced mathematical methods in spatial and time discretization of neutronics, heat transfer and two-phase flow hydraulics. The dynamic coupling with the thermal hydraulic system code SMABRE allows also the modelling of cooling circuits. Best-estimate or conservative analyses can be performed for different accidents, e.g. RIA, ATWS or local boron dilutions. The usefulness of the three-dimensionality is shown particularly when there are asymmetric changes in the fission power distribution originating from local neutronic or thermal hydraulic disturbances in the core or cooling circuits. The new hydraulics solution method PLIM developed at VTT has been applied in HEXTRAN to remove modelling restrictions and to eliminate numerical diffusion and dispersion.

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ISBN 951-38-4784-5 ISSN 1235-0621 UDC 621.039:681.3:621.039.4