A SURVEY OF NEW TRENDS IN NUCLEAR THERMAL-HYDRAULICS. (invited) Henrique Austregesilo Filho

Transcription

1 A SURVEY OF NEW TRENDS IN NUCLEAR THERMAL-HYDRAULICS (invited) Henrique Austregesilo Filho Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbh D , Garching, Germany ABSTRACT This paper presents an overview of the current capabilities of thermal-hydraulic computer codes used for the safety analysis of light water reactors (LWRs). It includes a description of application areas and of new development issues, and tries to point out some of the known code limitations. One of the most valuable sources of information about the status of the art in this area was the OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, held November 1996 in Annapolis, USA. This survey does not pretend to be complete, but it may be helpful to define needs and priorities for further developmental work in this field. I. INTRODUCTION Thermal-hydraulic computer codes are among the main computational tools for the safety analysis of nuclear power plants. They have been used in the last three decades for the evaluation and follow-up of reactor operation, for safety analyses required for licensing, and for supporting the design of new components and power plants. In the early 70 s safety evaluation was focussed on the analysis of Design Basis Accidents (DBA). The codes were based on a set of three conservation equations for a homogeneous two-phase steam-water mixture. One of the most widely used codes was RELAP4, mainly its evaluation model version, which complied with the Appendix K criteria. This code was the main code within the Water Reactor Evaluation Model (WREM) package [1]. At that time, a typical large break LOCA analysis was performed in several steps, with different codes. For instance, a blowdown analysis performed with RELAP4 was followed by a hand calculation of the refill phase and determination of the initial and boundary conditions for the reflood phase, simulated with the code RELAP4-FLOOD. The thermal-hydraulic boundary conditions generated by these codes were then used for the calculation of the hot rod behaviour with TOODEE-2, or for the evaluation of the maximum containment pressure and temperature with the code CONTEMPT. Conservative assumptions on initial and boundary conditions, as well as on the choice of model options, were used to compensate for uncertainties on code accuracy and modelling simplifications. The policy of using conservative assumptions has at least two handicaps : the conservative margins can be too large and increase the cost of the nuclear plant or of its operation, and the used assumptions may not be really conservative in the full range of physical events that can occur in the course of an accident. In parallel to code development, a large experimental program was created in order to generate actual test data for comparison with code predictions. This experimental data base stimulated the development of a more realistic, best estimate modelling of the related thermal-hydraulic phenomena. Besides that, the TMI-2 accident, in 1979, has shown the need of modelling accident scenarios beyond those usually defined for the analysis of DBAs. Therefore a new generation of computer codes has been developed, mainly on the basis of a two-fluid formulation, aiming for a more realistic simulation of twophase flow and phase separation phenomena. These codes have been continuously improved, and their range of application considerably enlarged. With the establishment of international working groups for code assessment and validation, together with the so-called user s clubs, the application of this new code generation became universal.

2 II. CURRENT CODE CAPABILITIES The best-estimate codes nowadays (e.g. ATHLET [2], CATHARE2 [3], RELAP5 [4] and TRAC [5]) are based on conservation equations written for a grid of computational nodes. Within each node, the time and space dependent conservation equations for mass and energy are solved separately for both phases, whereas the momentum conservation equations for both phases are solved across the boundary between nodes. Additional conservation equations for boron and non-condensable gases are also available within the codes. In general, the spatial simulation within pipes is one-dimensional, while the simulation within the reactor vessel varies from one dimensional up to fully three dimensional, depending on the computer code. The nodalization is flexible and defined by the code user. Several hundreds of computational nodes are normally used for the simulation of the primary and secondary systems of light water reactors. Code assessment and validation are performed on the basis of comparisons with experimental data coming from separate effect tests, integral test facilities (with scaling ratios from 1:2000 up to 1:1) and available plant data. They include a developmental assessment, performed by the code developers, and an independent assessment, performed on the basis of a frozen code version by individuals and organizations outside the code development organization. In the last years, several methods have been developed to define and quantify code accuracy and uncertainty (e.g. [6], [7], [8] ). The main fields of application of the current thermal-hydraulic codes are : follow-up of operating reactors audit of licensing analysis investigation of emergency operating and accident management procedures safety evaluation of advanced LWR designs application as process model within nuclear plant analyzer and engineering simulators. The ultimate goal of code development is to cover the whole spectrum of transients and accidents conceivable to occur in a LWR with only one system code. The computer codes nowadays are not restricted to the simulation of the thermal-hydraulic processes within the reactor coolant system. The modelling of auxiliary and balance-of-plant systems, as well as of the reactor control and protection systems, has become an increasing priority within developmental efforts. The spectrum of postulated accidents is not bound anymore by the assumption of a single equipment failure. Events involving multiple failures or operator errors, under different initial conditions, from full power up to cold shutdown, are now analysed with the currently available codes. Besides that, the best estimate codes, which have been developed and assessed on the basis of western LWRs, are increasingly being applied to Russian-designed reactors, like VVERs and RBMKs. This extended range of applicability has generated new developmental work in the last years. The following sections try to point out some highlights of this work. Nuclear Plant Analyzers. The main thermal-hydraulic codes are being applied now as process models within nuclear plant analyzers (NPAs). This field of development intends to upgrade the simulation environment of the codes in order to increase the efficiency of analysis und understanding of plant behaviour. The NPAs can display transient results by means of user-designed pictures of the primary and/or secondary systems. The generated output data drive these pictures to show the state of the coolant system as the transient proceeds. By using color gradients to represent coolant conditions (e.g. temperature, voids, densities), the analyst can obtain an overall impression of the transient evolution. Other displays show the operating conditions of pumps, valves and safety systems. The NPAs can be used either in a playback mode or in an interactive mode. In the playback mode, the analyst can review a completed calculation at virtually any speed wanted, using features already known from training simulators (e.g. start, stop, freeze, replay). Trend curves of calculated parameters can also be displayed. In the interactive mode, the analyst can alter the boundary conditions of the calculations, much in the same way a reactor operator can interact with a power plant. This feature is especially useful for studying the efficacy of emergency and accident management procedures. Examples of NPAs driven by best-estimate codes are the RELAP5/NPA [9] and ATLAS [10]. The French simulator SIPA uses a speeded-up version of the CATHARE1 code, a former version of the CATHARE2 which uses the standard 6-equations model for the primary circuit of a PWR and a 3-equations model for the secondary circuit. It allows operator training or emergency studies with real time interactive simulation for a wide set of transients. Currently, work is in progress to incorporate CATHARE2 to plant analyzers without any simplification of the original models, in the frame of the SCAR (Simulator Cathare Release) Project [11]. An even more ambitious developmental project is the japanese simulation system IMPACT [12], started in 1993, for the realistic, detailed simulation of severe accidents in nuclear power plants. Coupling with 3D-Neutronics. The thermal-hydraulic analysis and the analysis of 3D neutronics behaviour have been developed as separated and complementary fields of nuclear safety analysis. Within the current thermalhydraulic codes, the reactor kinetics is simulated on the basis of a generalized space independent point kinetics model. This model is accurate enough for most transients

3 of interest, for which reactor shutdown is assumed to occur, or for small changes on radial and axial neutron flux profiles. The 3D reactor core behaviour is analyzed by neutronics codes solving the 3D neutron diffusion equations representing each fuel assembly of the core loading and describing feedback effects by fuel rods and coolant flow models corresponding to each fuel assembly. Meanwhile, the interest in coupling 3D neutronics models to thermal-hydraulic system codes has been growing considerably. Such coupled codes are required to simulate some specific accident sequences with initiating events like boron dilution transients, start-up of cold loops or control rod ejection, as well as ATWS (anticipated transients without scram) sequences with total or partial failure of reactor scram. Different strategies for coupling neutronics and thermal-hydraulics codes have been proposed. Basically, the thermal-hydraulic codes simulate the parallel flow channel in the core, and give the boundary conditions (fuel temperatures, coolant temperatures and/or densities and boron concentrations) for the calculation of the crosssections within the neutronics codes. These, in turn, calculate the generated neutron power for each node defined within the thermal-hydraulic codes. The mapping between thermal-hydraulic and neutronic nodes plays an essential role in this coupling strategy. Examples of coupling 3D neutronics and thermal-hydraulic codes can be found in [13-16]. Coupling with containment codes. For a detailed analysis of nuclear power plant behaviour during accident conditions not only the primary system (in-vessel) response but also the containment system (ex-vessel) behaviour must be accounted for. Usually, separate calculations are carried out with different codes. At a first step, a thermalhydraulic analysis of the reactor coolant system is performed, representing the containment as a fixed pressure boundary condition. The calculated mass and energy outflows, generally under choked flow conditions, are then used as input to the containment code. This procedure disregards the fact that containment conditions can influence in-vessel behaviour, for instance, in longterm accident sequences, or for transients like ATWS and steam line breaks in BWRs. Recently, efforts have been made to couple thermalhydraulic and containment codes. Different approaches have been proposed for the data transfer between codes and for time step coordination. The containment codes CONTAIN and COCO, for instance, have been sucessfully coupled to RELAP5 by means of the Parallel Virtual Machine (PVM) operating system [17] respectively through the general interface code EUMOD [18]. Both approaches are based on an explicit coupling at a time-step level, using the RELAP time step as the master time step for both codes. The current time values of the in-vessel parameters are calculated using the containment parameters from the previous time step. The PVM operating system controls the execution process and the data transfer. It is almost machine independent, and provides multi-processing capability on a loosely coupled computer network. For the data transfer in the PVM environment, many subroutines of both codes had to be modified, and new subroutines created, but without changes of the physics modelling. The EUMOD interface acts as a subroutine within the RELAP5 code. Data is transferred via a call to the EUMOD interface, and then to the coupled containment code. One advantage of this approach is the small amount of changes to the RELAP code needed for the coupling. On the other hand, since the coupled codes and the interface EUMOD run in the same machine, this coupling approach requires more memory and disc storage. A similar approach has been chosen for the coupling between ATHLET and the containment code CONDRU [19]. This coupling has been performed by means of a general interface to a library of external dynamic simulation models, with own input and output data, provided by the General Control Simulation Module (GCSM) within ATHLET. It allows the on-line calculation of pressure and temperature within the containment using as boundary conditions the calculated mass and energy flow rates through breaks and/or safety and relief valves, as well as the consideration of the actual containment pressure for the calculation of the discharge mass flow rate. Control systems and balance-of-plant (BOP) models simulated within GCSM can be used in both codes. III. BEYOND DBA ANALYSIS A key developmental area is the extension of code simulation capability towards severe accident analysis. The main objective is to describe mechanistically not only the thermal-hydraulic response of the reactor coolant system (RCS) but also the core damage progression and the fission products transport and release during severe accidents within only one modular code architecture. The best known system code for BDBA analysis is SCDAP/RELAP [20]. It combines models coming from the codes RELAP5, SCDAP and COUPLE. The RELAP5 portion of the code calculates the overall RCS behaviour, including fluiddynamics, reactor kinetics, control system behaviour and one-dimensional heat conduction in RCS pipes, structures and in lower temperature vessel structures. The SCDAP portion of the code calculates the heatup and damage progression in the core and surrounding structures, including the upper plenum structures, shroud and lower core plate. It simulates the heating, deformation, oxidation and melting of fuel rods, control rods and other structures using a two-dimensional approach, the formation, heating and melting of debris

4 using a lumped-parameter approach, as well as the growth and relocation of molten pool materials. The COUPLE portion of the code uses twodimensional, finite elements to describe the accumulation, heating and melting of debris and associated lower plenum structures, the formation and growth of molten pools, and the failure of the lower head due to thermal and creep rupture mechanisms. The data transfer between modules takes place at every time step, by means of common blocks. The geometrical parameters (e.g. areas, hydraulic diameters and volumes) of the RELAP control volumes in the core region and lower head are adjusted by SCDAP to account for changes in geometry caused by fuel rod ballooning, fuel rod and control rod meltdown, and slumping of core material to the lower plenum. The RELAP5 volumetric source term for steam and non-condensable gases are updated by SCDAP to account for hydrogen production and steam removal due to oxidation of fuel elements, and the release of fission gases from the rods. A similar modular approach has been used for the development of the severe accident system code ATHLET- CD [21]. This code consists of four general modules : the RCS thermal-hydraulics module ATHLET, the core degradation module ECORE, the fission product (FP) release module EFIPRE, and the FP and aerosol transport module TRAPG. The module ECORE simulates core heatup, melting and relocation, and includes models to describe the behaviour of fuel rods, PWR control rods (AIC or B 4 C as absorver), and BWR channel boxes and control elements. The module EFIPRE embodies the description of FP release based on rate equations, FP diffusion in fuel grain and fuel pellets, as well as FP gap release. The initial inventory can be defined by user input or calculated by a preprocessor (e.g. ORIGEN). TRAPG contains, besides the FP and aerosol transport module of TRAPMELT, a new module, SOPHAEROS, to describe simultaneously transport, deposition, agglomeration, resuspension and chemical reactions of FP and aerosols. The current range of application of ATHLET-CD covers the in-vessel thermal-hydraulics, the early phase of core degradation, as well as FP and aerosol release and their transport within the reactor coolant system for Western and Eastern LWRs. Another example of coupled severe accident and thermal-hydraulic best-estimate codes is given by the coupled code ICARE2 / CATHARE2 [22]. ICARE2 is a mechanistic code for the description of phenomena occuring in the core region during the early phase of core degradation, including thermal and mechanical behaviour of the fuel and control rods (ballooning, melting and relocation), chemical interactions and fission product release. ICARE2 has been introduced into CATHARE2 as a new module, acting as a core element, with one or more core flow channels, connected to adjacent CATHARE2 elements through junctions. The calculation is driven by CATHARE2, which defines the inlet and outlet boundary conditions for each core channel. An alternative approach for the simulation of severe accidents is the use of the so called integrated codes. These codes describe the whole severe accident in a nuclear plant, but they are based on a quite simplified modelling not only with respect to the nodalization but also to the description of two-phase flow phenomena. They produce fast and approximate results, whose accuracy decreases significantly as the transient proceeds. Detailed mechanistic codes should be preferred, even though they still need extensive improvements and assessment for the later phase of core degradation, with the relocation of core debris into the lower plenum and with lower head failure. IV. SOME LIMITATIONS AND FURTHER DEVELOPMENT NEEDS Constitutive Equations. The two-fluid formulation of the best-estimate codes requires closure relationships to describe the interaction of the phases with each other and with the system boundaries. Constitutive equations are needed for the calculation of, e.g., interfacial mass transfer rates, interfacial drag coefficients, fluid-wall drag coefficients, and interfacial or wall-to-fluid heat transfer coefficients. These closure relationships, derived either empirically or based on theoretical considerations, have a limited range of validity, corresponding to the range of the experimental parameters used for their derivation, and should not be extrapolated beyond these limits. However, extrapolations are not explicitly avoided in the current codes. One of the limitations of the current codes is the use of flow regime maps. They are applied to define the interfacial area concentration and the phase-wall contact area. These empirically-based maps were developed on the basis of steady-state fully developed flow. This steady-state assumption is often applicable to transient simulations, but flows inside major parts of the reactor coolant system are never fully developed. Entrance effects on the distribution of steam and water are not taken into account. Since the evolution of a flow pattern is not described dynamically and relaxation times are not taken explicitly into account, wide transition regions must be defined in order to avoid numerical instabilities. Besides that, a great amount of the experimental data base for the flow maps has been obtained from adiabatic air-water experiments, at or near atmospheric pressure, and often in small-scale test rigs. Multi-Dimensional, Multi-Field Simulation. The bestestimate codes, like RELAP5 and ATHLET, are basically limited to one-dimensional flow conditions. Twodimensional situations are simulated approximately by

5 parallel channels or single branch components, connected by cross-flow junctions. TRAC and CATHARE have special 3Dcomponents, but the closure relationships used in 3Dmodels are generally an extrapolation from 1D-models. This may lead to shortcomings, since quantities averaged over cross-sections do not have the same meaning as local values. Currently, only diffusion toward wall or interface can be correlated. The internal turbulent diffusion inside each phase is either not modelled or it is modelled by simple mixing length assumptions. Although multi-dimensional simulation of single phase flow (CFD-codes) has reached a certain degree of maturity, supported by the immense development of computational capabilities, the derivation of sound closure relationships for multi-dimensional two-phase flow models is still at its beginning. The present knowledge of turbulence modelling in two-phase flow (k,e - approach) is limited to dispersed flow. Besides that, the current codes generally use a firstorder scheme for the spatial discretization, either with finite volumes or by means of finite differences with staggered meshes. Although stable, the first-order scheme can be a source of numerical diffusion. A typical example is the relatively poor accuracy for the prediction of sharp propagation fronts, for instance, in boron dilution transients. Another limitation is the consideration of only two fields for all flow pattern situations : a liquid field for the water, and a gas field for steam and non-condensable gases. During a large break LOCA, for instance, core reflooding could be more accurately described by two liquid fields : a liquid film and a droplet field, in order to predict physical phenomena like liquid entrainment and de-entrainment in the upper plenum, which can strongly influence the quench front propagation. Advanced Light Water Reactors. New design features are currently being considered to improve the safety of a new generation of nuclear power plants. Several new reactor concepts with passive safety features are being developed. The proposed advanced LWRs, like AP600, SBWR or the European project EPR share some common characteristics. They rely on passive safety systems to reach a safe shutdown state following an accident. Large, in-containment water sources, driven solely by gravity are planned to make-up any lost coolant. These new designs rely on the depressurization of the primary system below containment pressure in order to allow gravity driven safety injection into the core region, and to avoid the risks of high pressure core melting. Low pressure phenomena are thus dominant in ALWR safety analyses. Several modelling challenges for the current thermal-hydraulic codes have been identified [23]. They include : steep temperature gradients in tanks, pools and large horizontal pipes (thermal stratification modelling) steam condensation in the presence of non-condensable gases small, gravity-driven pressure forces constitutive equations in low pressure, low flow ranges (heat transfer, interfacial drag) calculation of long-term transients (up to several days). User s Influence on Calculated Results. It is a well known fact that the code user has a strong influence on the quality of the calculated results. These user effects have been identified in the international standard problem exercises, where participants using the same code version obtained significantly different results [24]. Some of the potential sources of user effects during the preparation of an input data set for a given application are : the development of an adequate nodalization scheme, very often a compromise between accuracy and computational effort the choice of code options and model parameters the determination of input parameters needed for specific, mainly empirical component models, like homologous curves for pumps, or characteristic curves for steam-water separators. the selection of parameters controlling time step size and numerical accuracy the specification of initial and boundary conditions. An important task for current and future code development is to reduce the user s influence on calculated results. Some measures can be : extended guidelines for system mapping, nodalization and choice of model options (if they are not avoidable at all) enhanced input checking and run diagnostics improved user interface, with high-performance graphic tools, and on-line access to code documentation. V. FINAL REMARKS The current thermal-hydraulic codes have shown their applicability to a wide spectrum of accident scenarios in LWRs. However, they still have a potential for further development. Code limitations, either with respect to the basic modelling approach or to the applied numerical methods, can strongly contribute to the uncertainty of code predictions. The breath-taking development of computational capabilities, the progress in local instrumentation technology for two-phase flow, the increasing interest in advanced, inherently safe reactors and the continuous extension of accident scenarios beyond the range of applicability of current codes may promote the

6 development of a new generation of thermal-hydraulic computer codes. This new generation of thermal-hydraulic codes shall apply modern software engineering principles (more efficient coding, better matrix solution methods, vectorization, parallelization). The codes shall be more efficient, robust, and user-friendly, running mainly on a simulator environment. Less time will be needed to generate plant models and to evaluate the calculated results. The quantification of code uncertainties will be an essential part of the overall code assessment process. REFERENCES [1] Throm, E. D., WREM - Water Reactor Evaluation Model - Revision 1, Division of Technical Review of Nuclear Regulatory Commission, May [2] Lerchl, G. and Austregesilo, H., ATHLET Mod 1.1 Cycle C - User s Manual, GRS-P-1 / Vol. 1, [3] Barre, F. et al., New Developments in the CATHARE 2 Code, NURETH 6, STR/LML-EM/94-210, Grenoble, France, [4] RELAP5 Development Team, RELAP5/MOD3 Code Manual, Vols. 1-7, NUREG/CR-5535, Idaho National Engineering Laboratory, USA, [5] Spore, J. W. et al., TRAC-PF1/Mod 2 - Code Manual, Vols. 1-4, NUREG/CR-5673, [6] Boyack, B. E. et al., An Overview of the Code Scaling, Applicability and Uncertainty Evaluation Methodology, Nucl. Eng. Des., 119, 1,1990. [7] Glaeser, H. et al., Uncertainty and Sensitivity Analysis of a Post-Experiment Calculation in Thermal Hydraulics, SMIRT-12, Post Conference Seminar No. 15, Heidelberg, Germany, [8] D Auria, F., Debrecin, N., and Galassi, G. M., Outline of the Uncertainty Methodology based on Accuracy Extrapolation (UMAE), OECD-CSNI Special Workshop on Uncertainty Analysis Methods, London, UK, [9] Johnsen, G. W. and Riemke, R. A., Methodology, Status and Plans for Development and Assessment of the RELAP5 Code, OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, USA, Nov [10] Beraha, D. and Voggenberger, T., Fundamentals and Main Features of the German NPA Project ATLAS, Proc. Of the 1989 Eastern Multiconference / Simulators VI, Tampa, USA, March [11] Faydide, B., Current and Planned Numerical Development for Improving Computing Performance for Long Duration and/or Low Pressure Transients, OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, USA, Nov [12] Vierow, K. et al., The IMPACT Super Simulator - Basic Framework, Proc. of the 1995 Simulation Multiconference / Simulators XII, Phoenix, AZ, USA, Apr [13] Langenbuch, S., Lizorkin, M., Rohde, U. and Velkov, K., 3D Neutronic Codes Coupled with Thermal-Hydraulic System Codes for PWR, BWR and VVER Reactors, OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, USA, Nov [14] Judd, J. L. et al., High Fidelity Real Time Simulation with RELAP5/NESTLE, Trans. Amer. Nucl. Soc., 75, Nov [15] Page, R., Development of an Integrated Thermal-Hydraulics Capability Incorporating RELAP5 and PANTHER Neutronics Code, OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, USA, Nov [16] Takeuchi, Y. et al., TRACG Transient Analysis Code - Three Dimensional Kinetics Model Implementation and Application for Space - Dependent Analysis, Nucl. Technology, 105, p. 162, [17] Smith, K. A., Baratta, A. J. and Robinson, G. E., Coupled RELAP5 and CONTAIN Accident Analysis Using PVM, Nucl. Safety, 36, p. 94, [18] Rothe, T., Linking External User Models to RELAP5 : A New Era of RELAP5 Applications, Proc. of the International Conference on New Trends in Nuclear Systems Thermohydraulics, Pisa, Italy, vol. I, 263, [19] Austregesilo, H., Kirmse, R., Tiltmann, M. and Macek, J., Analysis of a Large Break LOCA in the Hot Leg of a WWER-1000 Plant for the Prediction of Containment Pressure, Proc. of the Sixth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, NURETH 6, vol. 2, 984, Grenoble, France, Oct [20] SCDAP / RELAP5 / Mod 3.1 Code Manual, Volumes 1-5, NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, June 1995.

7 [21] Bestele, J. and Trambauer, K., Status of ATHLET-CD Development Shown by the LOFT-FP-2 Analysis as an Example, Int. Symposium on Heat and Mass Transfer in Severe Reactor Accidents, Cesme, Turkey, May [22] Camous, F., Jacq, F., Chatelard, P. and Flores, J. M., Interface Requirements to Couple Thermal Hydraulic Codes to Severe Accident Codes : ICARE / CATHARE, OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, USA, Nov [23] Kelly, J. M., Thermal-Hydraulic Modeling Needs for Passive Reactors, OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, USA, Nov [24] Aksan, S. N., D Auria, F. and Städtke, H., User Effects on the Thermal-Hydraulic Transient Code Calculations, Nucl. Eng. and Design, 145, p. 159, 1993.