Simulation of the chernobyl accident

An analysis of the April 26, 1986 accident at the Chernobyl-4 nuclear power plant in the Soviet Union is presented. The peak calculated core power during the accident was 550 000 MW_t. The analysis provides insights that further understanding of the plant behavior during the accident. The plant was modeled with the RELAP5/MOD2 computer code using information available in the open literature. RELAP5/MOD2 is an advanced computer code designed for best-estimate thermal-hydraulic analysis of transients in light water reactors. The Chernobyl-4 model included the reactor kinetics effects of fuel temperature, graphite temperature, core average void fraction, and automatic regulator control rod position. Preliminary calculations indicated the effects of recirculation pump coast down during performance of a test at the plant were not sufficient to initiate a reactor kinetics-driven power excursion. Another mechanism, or “trigger” is required. The accident simulation assumed the trigger was recirculation pump performance degradation caused by the onset of pump cavitation. Fuel disintegration caused by the power excursion probably led to rupture of pressure tubes. To further characterize the response of the Chernobyl-4 plant during severe accidents, simulations of an extended station blackout sequence with failure of all feedwater are also presented. For those simulations, RELAP5/MOD2 and SCDAP/MOD1 (an advanced best-estimate computer code for the prediction of reactor core behavior during a severe accident) were used. The simulations indicated that fuel rod melting was delayed significantly because the graphite acted as a heat sink.     

A review of modeling concepts for sodium-concrete reactions and a model for liquid sodium transport to the unreacted concrete surface

A review of existing modeling concepts and studies of sodium-concrete reactions is presented. Consistent with experimental observations, the current modeling study being conducted at Hanford Engineering Development Laboratory assumes for hydrated concretes the presence of liquid layer of reaction products intervening between sodium pool and concrete surface. Primary liquid component in this layer is NaOH which has a low melting point. This liquid component dissolves the reaction products such as silicates, aluminates and forms a very viscous liquid more dense than sodium. As this layer assumes a significant thickness, the only mechanism available for transport of sodium to fresh concrete surface is the motion and agitation induced by gas bubbles consisting of hydrogen, water vapor, CO₂ and sodium vapor. However, to date there exists no satisfactory model that describes this transport mechanism. To rectify this shortcoming, we propose a mass “iffusion” model for sodium transport. The model reduces the sodium transport process by bubble motion to a single unknown parameter which has the appearance of a diffusion coefficient and consequently can be determined by solving an inverse problem in conjunction with measured “concentration” distributions in simulant material experiments.     

The AREVA HTR fuel cycle: An analysis of technical issues and potential industrial solutions

The AREVA high temperature reactor (HTR) is a modular 600 MWt high temperature gas-cooled reactor that provides up to 950 °C process helium for power generation and/or hydrogen production. Energy facilities based on this technology will consist of up to four AREVA HTR modules achieving high thermodynamic efficiency with a total possible electrical generation capability of 1200 MWe. At the heart of the AREVA HTR is the TRISO-coated low-enriched uranium (LEU) fuel which is assembled into fuel compacts that are inserted into prismatic graphite fuel elements.The intent of this paper is to examine the AREVA HTR fuel and fuel cycle from two perspectives. First, from the “front-end” perspective, the available fuel cycle-related options are examined along with the basis for the subsequent choice of fuel type and cycle. Second, from the “back-end” perspective, the generation and management of spent fuel and graphite waste is examined along with the strategies and options available for disposition or disposal.The AREVA HTR has the inherent flexibility to accommodate many fuel types and to permit full cost-effective optimization. The reasons for this flexibility are presented and the main advantages and disadvantages of the various fuels cycle are discussed. The reference fuel cycle for the AREVA HTR is then introduced and its main features are given. Additionally, non-proliferation attributes of the AREVA HTR technology are also examined.The amount of spent fuel and graphite waste generated by the AREVA HTR is governed by the burn-up capability of the fuel and the longevity of the adjacent graphite reflector blocks. As currently envisioned, the AREVA HTR will need to be refueled every 18 months, with 50% of the core being replaced. Additionally, the graphite reflector blocks will need to be replaced at regular intervals. Given a 60-year design life, approximately 20,000 spent fuel elements and 10,000 graphite reflectors blocks will be generated. The near-term and long-term options for dealing with these waste streams are examined and, as with the front end of the fuel cycle, a reference strategy for spent fuel and graphite waste proposed.     

PSB-VVER simulation of Kozloduy NPP “loss of feed water transient”

This paper provides a comparison between the PSB test facility experimental results obtained during the simulation of loss of feed water transient (LOFW) and the calculation results received by INRNE computer model of the same test facility. Integral thermal-hydraulic PSB-VVER test facility located at Electrogorsk Research and Engineering Center on NPPs Safety (EREC) was put in operation in 1998. The structure of the test facility allows experimental studies under steady state, transient and accident conditions.RELAP5/MOD3.2 computer code has been used to simulate the loss of feed water transient in a PSB-VVER model. This model was developed at the Institute for Nuclear Research and Nuclear Energy for simulation of loss of feed water transient.The objective of the experiment “loss of feed water”, which has been performed at PSB-VVER test facility is simulation of Kozloduy NPP LOFW transient. One of the main requirements to the experiment scenario has been to reproduce all main events and phenomena that occurred in Kozloduy NPP during the LOFW transient. Analyzing the PSB-VVER test with a RELAP5/MOD3.2 computer code as a standard problem allows investigating the phenomena included in the VVER code validation matrix as “integral system effects” and ”natural circulation“. For assessment of the RELAP5 capability to predict the “Integral system effect” phenomenon the following RELAP5 quantities are compared with external trends: the primary pressure and the hot and cold leg temperatures. In order to assess the RELAP5 capability to predict the “Natural circulation” phenomenon the hot and cold leg temperatures behavior have been investigated.This report was possible through the participation of leading specialists from Kozloduy NPP and with the support of Argonne National Laboratory (ANL), under the International Nuclear Safety Program (INSP) of the United States Department of Energy.     

The influence of the chemical state of the fission products on the filter properties of the graphite components

Results from the experimental and theoretical studies on the transport and sorption behaviour of Cs in graphite with and without oxygen impurities and in the case of HTR-relevant accident conditions are presented and compared. The transport mechanisms of Cs in graphite are discussed on the basis of the calculations carried out with the PATRAS-CORE computer program and the experimentally determined effects dealt with in detail theoretically. Finally, the consequences arising for the safety of an HTR plant are analyzed.     

Prediction of fuel channel—graphite gas-gap behaviour in RBMK reactors

To maintain thermal contact between the fuel assembly and the graphite moderator, RBMK design reactors employ graphite split rings, which are alternatively tight on the pressure tube or tight on the graphite brick central bore. The split in the graphite rings allows a helium/nitrogen gas mixture to flow up the fuel channel. This prevents oxidation of the graphite and can be sampled to detect pressure tube leaks. The initial clearance between the rings and pressure tube or graphite brick is approximately 2.7 mm (1.35 mm each side). Due to material property changes of the pressure tubes and graphite during operation of the reactor, the size of the clearance between the rings and the pressure tube/brick, called the “gas-gap”, varies. Closure of these gaps has been identified as a possible safety case issue by reactor designers and by independent reviews carried out as part of TACIS reviews and as part of the Ignalina Safety Analysis Report. The reasons for this are that gas-gap closure would cause the pressure tube to be tightly gripped by the graphite bricks via the split rings, which could lead to:

• Extra loading on the upper pressure tube zirconium/steel transition joint, particularly during shut down and emergency transients.

• Splitting of the graphite brick, leading to loss of thermal contact between the pressure tube and graphite. As approximately 5.6% of the heat in graphite-moderated reactor is generated within the moderator through neutron and gamma-heating, loss of thermal contact would result in higher graphite temperatures, accelerating the rate of graphite expansion and hence increasing the loading of the core radial restraint.

• Graphite debris may become lodged in inter-brick gaps, leading to increased axial pressure tube loading during shut down and emergency transients.

The authors have carried out deterministic assessments based on the Ignalina RBMK-1500 reactors in Lithuania, modelling the behaviour of the graphite under irradiation and have predicted graphite bore diameter changes that are in good agreement with the measurements of graphite bore diameters taken at Ignalina Nuclear Power Plant (NPP). A probabilistic model has been developed using the actual results of the deterministic calculations with non-linear graphite behaviour. Statistical analysis of the measurements of tube and graphite diameters taken from Units 1 and 2 at Ignalina NPP has been carried out. Further work has been carried out to try to determine the uncertainty inherent in the predictions of the gas-gap closure from the calculations. The overall objective of the studies is to aid prediction of the gas-gap closure process, and help to identify a suitable monitoring strategy for gas-gap closure that could be used for any RBMK reactor.     

Identification and modeling of nonlinear systems

A nonparametric identification technique is presented for use with discrete multidegree of freedom nonlinear dynamic systems of the type encountered in nuclear reactor technology. The method requires information regarding the system response and estimates of its pertinent “mode shapes” to determine, by means of regression techniques involving the use of two-dimensional orthogonal functions, an approximate expression for the system generalized restoring forces in terms of the corresponding generalized system state variables. For the special class of nonlinear systems that have chain-like characteristics, drastic simplifications in the procedure are realized, and the identification task can be easily and accurately accomplished without using any information regarding estimated “mode shapes”. The technique is applied to several example systems. The method can be used with deterministic or random excitation to identify dynamic systems with arbitrary nonlinearities, including those with hysteretic characteristics. It is also shown that the method is easy to implement and needs much less computer time and storage requirements compared to the Wiener-Kernel approach.     

Methodologies for rapid evaluation of seismic demand levels in nuclear power plant structures

A methodology for rapid assessment of both acceleration spectral peak and “zero period acceleration” (ZPA) values for virtually any major structure in a nuclear power plant is presented. The methodology is based on spectral peak and ZPA amplification factors, developed from regression analyses of an analytical database. The developed amplification factors are applied to the plant's design ground spectrum to obtain amplified response parameters. A practical application of the methodology is presented.This paper also presents a methodology for calculating acceleration response spectrum curves at any number of desired damping ratios directly from a single known damping ratio spectrum. The methodology presented is particularly useful and directly applicable to older vintage nuclear power plant facilities (i.e. such as those affected by USI A-46). The methodology is based on principles of random vibration theory. The methodology has been implemented in a computer program (SPECGEN). SPECGEN results are compared with results obtained from time history analyses.     

A bubble number density constitutive equation

A statistical formulation is used to describe gas-liquid two-phase flows. It is shown that this kind of flow cannot be considered a dilute system as is currently done. A correction factor, the pair correlation function, is introduced to account for “dense effects”. Integrating the transport equation of the bubble volume distribution function over all possible volumes, a number density transport equation is obtained, which explicitly accounts for bubble breakup and coalescence phenomena. A complete model is constructed in conjuction with the mass and momentum conservation equations. Its predictions were compared with experimental results on bubble columns. Excellent agreement was found. The theoretical model was able to predict the void fraction axial distributions, which showed strong variations.     

Fuel behaviour models incorporated in COMETHE III-J

Some of the fuel behaviour models incorporated in the COMETHE III-J computer code are reviewed. The fuel swelling model is first described and each of its components is discussud. The fuel restructuring calculation takes equiaxed or columnar grain growth into account. Grain growth and gaseous swelling are coupled in a realistic way to the gas release model. One of the milestones of the COMETHE III-J code is the crack pattern calculation by means of the “pivot” concept. This model couples cracking with thermal expansion and three-dimensional plasticity effects. The effects of radial and axial restraints, coupled with fuel swelling or densification resulting from columnar grain growth, account for fuel relo cation and dish, crack or central hole filling. The power cycling effects are therefore naturally modelled and no additional relocation is required to explain the gap closure.     

Advances in two-phase flow modeling for LMFBR applications

This paper summarizes the development of numerical models for analysis of sodium boiling phenomena in LMFBR which has been carried out at M.I.T. over the last five years.With regard to the degree of spatial averaging, our models use the porous body approach, in two and three-dimensional configurations. One important advantage of this model is the ability to accommodate homogenization of arbitrary-sized regions of interest.From a numerical point of view our basic approach is a semi-implicit method in which pressure pulse propagation and local effects characterized by short time constraints are treated implicitly, while convective transport and diffusion heat transfer phenomena, associated with longer time constants, are handled explicitly. This method remains tractable and efficient in multi-dimensional applications.Both a six-equation (“two-fluid”) model and a four-equation (“mixture”) model have been pursued. A considerable effort has been devoted to the development of constitutive relations. Our current package provides an adequate simulation capability for a wide range of applications.This paper will present the general physical formulation of the codes, the constitutive relations, the general numerical approach, applications, and finally some concluding remarks based on our experience with these codes.     

The use of energy absorbers to protect structures against impact loading

When a flying missible impacts a fixed structure, the interface loading is dependent on the deformation characteristics of both impacting and impacted bodies. If both are too rigid to accommodate the amount of gross deformation required to neutralize the incoming kinetic energy, or if such energy absorption has a chance to proceed in uncontrolled and unreliable ways, then there is a need to interpose a specifically designed “energy absorber” between missile and structure, from which a well-defined load time history can be derived during the course of impact.

The required characteristics of such an energy absorption material are:

• the capability to accommodate large permanent deformation without structural failure; and

• the reliable and controlled “load-deformation” (or “stress-strain”) behaviour under dynamic conditions, with an aim at an optimal square shape curve.

Consideration must also be given to environmental or other disturbing effects, like temperature, humidity, and “out of plane” loading. A short survey is presented of the wide range of energy absorbers already described in technical papers or used in a number of practical safety applications within varied engineering fields (from vehicle crash barriers to high energy pipe whipping restraints). However, with such open a literature, information is usually lacking in the specific data required for design analysis.

The following “energy absorption” materials and processes have thus been further experimentally investigated, with an a aim at pipe whipping restraint application for nuclear power plants:

1. (1) plastic extension of austenitic stainless steel rods;

2. (2) plastic compression of copper bumpers; and

3. (3) punching of lightweight concrete structures.

Dynamic “stress-strain” characteristics have been established for stainless steel bars at several temperatures under representative loading conditions. For this purpose, a test rig has been specifically designed to incorporate a number of adjustable parameters and to behave as a representative “slice” of an actual pipe whipping restraint; typical strain rates are in the 10 sec⁻¹ range. The behaviour of copper bumpers has been compared under static and dynamic conditions (using a conventional drop weight test (DWT) machine); as no significant strain rate effects were emphasized, only static tests have been further developed. The DWT rig was used again to investigate crushing or punching of cellular concrete under varying geometries and loading conditions. To remedy certain deficiencies of the regular commercial grades of cellular concrete, special lightweight mixtures have been studied to optimize material toughness and provide a wider range of specific resistance.Results of this experimental program are presented and discussed. The use of energy absorbers is then illustrated for a few typical pipe whipping restraints. The design of restraints is based on real dynamic characteristics of “energy absorption” material as produced by the test program. To derive design loads of restraints, a number of methods can be used ranging from a simplified “energy balance” graph to sophisticated plastodynamic computer analysis. Typical results are presented and discussed to compare the efficiency of these alternative methods.     

Iodine removal by condensation from containment atmosphere in post external event conditions

An integral solution is derived for the problem of passive removal rate of a typical fission product (iodine), from a gas-vapor mixture, by condensate liquid film adjacent to a containment wall. The analytical model consists of a coupled set of five conservation equations: momentum, energy and three matter conservation equations for each individual component of the gas mixture: air, steam and elemental iodine. The set is solved in conjunction with two balance equations for the mass and energy transport at the interface with the condensate layer. The model accounts for free convection due to temperature and concentration gradients, for mass and thermal diffusion and for variable properties in both the liquid and the gas-vapor regions. An economic solution procedure of this model is presented and employed for a wide range of parameters. The computational results of this study are used to derive an efficient correlation which provides a quick and simplified means of the calculation of the iodine mass removal coefficient, as a function of the bulk conditions. Some results are compared to other theoretical and experimental works showing good agreement within about 10%. The significance of the removal process in the “external event” scenario is analyzed and found to be much higher than in scenarios that start with a mechanical failure in the primary system.     

Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid–structure-interaction coupling

A homogenisation method is presented and validated in order to perform the dynamic analysis of a nuclear pressure vessel with a “reduced” numerical model accounting for inertial fluid–structure coupling and describing the geometrical details of the internal structures, periodically embedded within the nuclear reactor. Homogenisation techniques have been widely used in nuclear engineering to model confinement effects in reactor cores or tubes bundles. Application of such techniques to rector internals is investigated in the present paper. The theory bases of the method are first recalled. Adaptation of the homogenisation approach to the case of rector internals is then exposed: it is shown that in such case, confinement effects can de modelled by a suitable modification of classical fluid–structure symmetric formulation. The method is then validated by comparison of 3D and 2D calculations. In the latter, a “reduced” model with homogenised fluid is used, whereas in the former, a full finite element model of the nuclear pressure vessel with internal structures is elaborated. The homogenisation approach is proved to be efficient from the numerical point of view and accurate from the physical point of view. Confinement effects in the industrial case can then be highlighted.     

Dynamic model for control system design and simulation of a low temperature nuclear reactor

A lumped parameter dynamic model for the primary-loop and the U-tube steam generator of a low temperature power reactor is developed based on the fundamental conservation laws of fluid mass, energy and momentum. The dynamic model is formulated by coupling the point kinetics with reactivity feedback and the thermal-hydraulics of the reactor. The developed dynamic model is implemented on a personal computer using MATLAB/SIMULINK. Numerical simulation results for steady-state and transient responses are then presented, which show that the steady-state precision of the newly developed dynamic model is acceptable and the trend of the transient responses is correct. In addition, the “swell and shrink” behavior of the U-tube steam generator is also verified by numerical simulation. This newly established model can be utilized to control system design and simulation for the low temperature power reactor.     

On the zero-energy moments of the distribution of fast atoms and cascades

The slowing down of neutrons in capture-free hydrogen is not only a classic problem in transport theory but is a paradigm for several problems in the interaction of energetic ions with matter. Here we are concerned primarily with the distribution of stopped particles. We describe a novel expansion for the transport equation which which gives extremely accurate results for the moments of the distribution and which proves an earlier conjecture made by E.M. Baroody. We discuss additional applications of the expansion, which appears to be an improved “straight-ahead” approximation.     

Large-scale numerical simulation of mechanical and thermal properties of nuclear graphite using a microstructure-based model

The mechanical and thermal properties of nuclear graphite depend strongly on the microstructures. In this paper, a large-scale three-dimensional boundary element model is presented to study the relationships between the bulk effective properties and microstructure changes in nuclear graphite. Acceleration of the associated boundary element method (BEM) is achieved by use of a fast multipole method (FMM) in allowing large-scale numerical simulations of the model containing up to several hundred micro-structural pores to be performed on one desktop computer. The effects of several key micro-structural parameters such as the pore aspect ratio and the fractional porosity on the bulk mechanical and thermal properties of nuclear graphite are evaluated. The numerical results are compared with some experimental data due to oxidation and good agreement is observed. It is demonstrated that the presented method is potential for fundamental understanding of the bulk properties of nuclear graphite from micro-structural views.     

The frequency-dependent elements in the code SASSI: A bridge between civil engineers and the soil–structure interaction specialists

After four decades of the intensive studies of the soil-structure interaction (SSI) effects in the field of the NPP seismic analysis there is a certain gap between the SSI specialists and civil engineers. The results obtained using the advanced SSI codes like SASSI are often rather far from the results obtained using general codes (though match the experimental and field data). The reasons for the discrepancies are not clear because none of the parties can recall the results of the “other party” and investigate the influence of various factors causing the difference step by step. As a result, civil engineers neither feel the SSI effects, nor control them. The author believes that the SSI specialists should do the first step forward (a) recalling “viscous” damping in the structures versus the “material” one and (b) convoluting all the SSI wave effects into the format of “soil springs and dashpots”, more or less clear for civil engineers. The tool for both tasks could be a special finite element with frequency-dependent stiffness developed by the author for the code SASSI. This element can represent both soil and structure in the SSI model and help to split various factors influencing seismic response. In the paper the theory and some practical issues concerning the new element are presented.     

A steady flow gaseous core fission reactor

A heterogeneous system of reactor vessel and cooling section is proposed as an alternative method for power generation in a gaseous core fission reactor. The process of “dissociative density inversion” is introduced as a means to attain criticality conditions inside the reactor. Results are presented of the thermodynamic equilibrium between U---C---F---He gas and a solid graphite wall at very high pressures and temperatures and various values of the fluorine potential.