Two-phase flow models in unbounded two-phase critical flows

Referring to a Loss-of-Coolant Accident situation in LWRs, an analysis of the two-phase region just downstream from the broken pipe, in which a two-phase critical flow takes place, has been performed. A characterization of the flow pattern inside the unbounded two-phase jet is given considering:

• - jet's external shape, obtained by means of photographic pictures;

• - pressure profiles inside the jet, obtained by means of a movable “Pitot” gauge;

• - jet phase's distribution information, obtained by means of X-ray pictures.

Jet's X-ray pictures show the existence of a central high-density “core” gradually evaporating all around, which gives place to a characteristic “dart flow” the length of which depends on stagnation thermodynamic conditions.     

Pipe whip analysis for nuclear reactor applications

The main problems encountered in pipe whip analysis are discussed and the way the authors tried to solve them is described. Such problems are:

1. (a) Breakage locations: AEC criteria are presented and discussed.

2. (b) Force computations: The jet force intensities during the accident are computed following Moody's theory. A computer program makes such an analysis automatically. Forces consequent to a longitudinal and a circumferential break are calculated; The forces consequent to the longitudinal break are computed as a sum of the forces consequent to two circumferential breaks, a mitigation coefficient is assumed.

3. (c) Preliminary analysis: Provided that a ‘restraint solution’ is necessary (and the related criteria are briefly discussed), a tentative distribution of the restraints is computed by means of a simple energy balance between the work done by the jet forces and the work absorbed both in the pipe and the restraint. A computer program makes such an analysis automatically.

4. (d) Final solution appraisal: The tentative solution obtained in the initial step is re-evaluated by means of a detailed dynamic elastoplastic code (FRUSTA, which is described in the companion paper).

A typical example is given, the jet forces and a tentative restraint distribution are computed; the various models used in the final appraisal solution are described and the results are evaluated mainly in order to check the validity of the preliminary criterion.     

PSA as a tool for decision making

The question on “How safe is safe enough?” is being responded presently by deterministic criteria. Probabilistic criteria in support to more rational and less emotional decisions in regulatory and licensing issues, rationalization of resource allocation and research prioritization, among others, have a potential which is only marginally being explored.This paper discussed PSA limitations and proposes three areas for the use of PSA in decision making, namely:

1. (a) preventing accidents,

2. (b) mitigating accidents, and

3. (c) defining regulatory requirements.

Current activities of the International Atomic Energy Agency in these areas are mentioned.PSA studies depict clearly the uncertainties and this is viewed as a positive aspect, which is unique to the use of probabilistic methods.     

Structural integrity of lmfbrs including leak before break

The German Basis Safety Concept is an approach which allows the possibility of catastrophic failures to be excluded. It was developed in Germany to render the probabilistic approach unnecessary for safety cases relating to nuclear power plants. The process of evaluation started in 1972, and in 1979 the Basis Safety Concept was officially published and thus became a legal requirement for LWR plants. With appropriate modifications in regard of the particular features of LMFBR, this concept has also been applied to SNR 300. The “Structural Integrity Demonstration Concept” of SNR 300 is based on five principles:

• - Principle of quality by design and fabrication

• - Principle of multiple examination

• - Principle of worst case consideration

• - Principle of operating surveillance and documentation

• - Principle of verification and continuous development.

The same principles are taken over for SNR 2.The specific requirements on the components relevant to safety have to be defined at an early stage so that the components can be designed appropriately to the feasibility of the measures required by the concept.     

Current perspective on fast reactor containment

The concept of “containment” is to provide a series of physical barriers between the radioactive products of the fission process and the public. All nuclear reactors have several such barriers and LMFBRs have more than most. These barriers are, successively:

1. fuel, which retains fission products;

2. fuel cladding, which encloses the fuel;

3. sodium coolant, which absorbs fission products released through fuel caldding;

4. primary coolant boundary, which has energy absorption and leakage control capabilities;

5. containment building, hereafter referred to as containment, which provides the final engineered barrier for control of radioactive releases;

6. exclusion distance, which provides space for natural attenuation of radioactive releases before reaching the public.

These barriers, along with the design approaches and features which protect their integrity under normal and accident conditions, assure that the public is adequately protected from the potential hazards of radioactivity residing in the core. It is only in the case of hypothesized core disruptive accidents (HCDAs) that these successive barriers can be sufficiently threatened as to pose a significant threat to the public. These HCDAs involve an extremely low probability sequence of successive failures resulting in core cooling imbalances which lead to fuel overheating. Under such conditions, the fuel and cladding barriers can be lost and energy sources can be generated which threaten the primary coolant boundary and containment. This paper addresses current perspectives on containment of HCDAs with emphasis on the approach and programs in the US.     

Seismic instrumentation for nuclear power plants: An interpretative review of current practice and the related standard in Germany

The German nuclear safety standard KTA 2201: “Design of nuclear power plants against seismic events”, consists of the following parts: 1. basic principles; 2. characteristics of seismic excitation; 3. design of structural components; 4. design of mechanical and electrical parts; 5. seismic instrumentation; and 6. measures subsequent to earthquakes.While Part 1 was published in June 1975, Part 5 was approved by the Nuclear Safety Standards Commission — Kerntechnischer Ausschuss (KTA) — in June 1977. The other parts are still under development. The requirements of the safety standard KTA 2201.5 deal with

1. (a) number of location (number and location of acceleration recording systems for different sites, single-block plants and multi-block plants);

2. (b) characteristics of instruments (readiness and operation of instruments, margin or errors, dynamic and operation characteristics, duration of records, seismic switch);

3. (c) triggering and information (loss of electric power, start of the acceleration recording systems, threshold of acceleration for triggers and seismic switches, optical and acoustic information); and

4. (d) documentation (results of recordings, inspection and tests).

The purpose of this paper is to present some detailed requirements of the safety standard KTA 2201.5, with its philosophy, and compare these with corresponding requirements in the US. It will be shown that with relatively few instruments, which are very reliable in operation and in triggering, an optimum of data may be available after an earthquake.     

On the finite element solution of the three-dimensional tire contact problem

Starting from a theoretical analysis of the static contact problem “deformable body-rigid object” various solutions including the three-dimensional pneumatic tire contact problem are being discussed. The computed shapes and sizes of the footprint area as well as the load-deflection response are in good agreement with experimental results. The following approaches for a numerical solution are presented in this paper:

1. (1) Elimination method: This method is based on using the influence coefficient technique to compute the nodal forces as well as the footprint area by iteration applying a geometrical linear or nonlinear FE technique.

2. (2) ‘Nonlinear Programming’ technique: Recent developments in the theory of nonlinear optimization in abstract spaces suggest to describe the contact problem by a constrained optimization problem in function spaces. The minimization of the potential energy of the elastic body, the rigid obstacle being replaced by an operator constraint depending on the displacement functions, leads to three necessary conditions determining completely the equations of equilibrium, the contact zone and the pressure distributions in the contact zone. This result justifies the use of a nonlinear programming code to solve the discrete problem approximated by the method of finite elements.

3. (3) Variation of boundary conditions: This method is based on an incremental formulation including nonlinear geometry and variable boundary conditions.

Comparison of results of soil-structure interaction analyses based on time and frequency domain approaches with emphasis on treatment of damping

Comparison of results of soil-structure interaction analyses of the reactor building of a nuclear power plant using different analytical approaches and solution procedures is presented. The emphasis of the comparison was on the treatment of damping in these different approaches and procedures. An axisymmetric model of the reactor building was employed. The analyses were performed for the aircraft impact loadings. Two different locations were used for these loadings.The following four different sets of analyses were performed.

1. (1) Time-domain analysis using frequency-independent soil springs in conjunction with modal damping cut-off.

2. (2) Frequency-domain analysis using frequency-independent soil springs in conjunction with a complex modulus approach.

3. (3) Frequency-domain analysis using frequency-dependent soil-impedance coefficients in conjunction with a complex modulus approach.

4. (4) Frequency-domain analysis using frequency-dependent soil-impedance coefficients in conjunction with Rayleigh damping.

The frequency-independent soil springs were computed using the standard approach based on rigid base supported on an elastic layered half-space. The frequency-dependent soil impedance coefficients were computed in the form of a soil substructure matrix which included the uncoupled as well as the coupled terms. The computations were based on the use of a “flexible” base mat supported on a layered half-space. Unit dynamic loads, for each frequency, were applied to the layered half-space corresponding to each degree of freedom and the displacements were xomputed corresponding to all degrees of freedom. The compliance matrix so computed was inverted to obtain the impedance matrix for each frequency. The computations were repeated for all frequencies of interest for the aircraft impact loading.Floor response spectra were developed and compared at various floor elevations of the reactor building using the above four different sets of analyses. Conclusions were developed as a result of these comparisons.     

Benchmarking results of the COMETHE code

The validation of a code for fuel rod behaviour prediction requires a comparison of its results with corresponding experimental data. Benchmarking of the COMETHE code has been done in parallel with its development, but more time has been spent on that work than in the development of the models themselves. Three experiments are presented; they have been selected from amongst those used by BN for the calibration as being good examples of various features:

1. (1) The ELP2 experiment, performed in the EL3 reactor by CEA-Saclay and related to fuel restructuring. Results show that behaviour is very well modelled in COMETHE.

2. (2) The BR3/VN post-irradiation data, which show a large sensitivity of the fission gas release to the power level and reveal that coupling between the fission gas release model and the gaseous swelling model is beneficial.

3. (3) The BM01 low density fuel BN pin, irradiated in the FBR RAPSODIE: close agreement is found between the cracking pattern computed by the “pivot model” and the experimental cold state results.

A lot of the benchmarking results arise from the EPRI RP 397 Fuel Rod Modeling Code Evaluation Project.     

SEMER: a simple code for the economic evaluation of nuclear and fossil energy-based power production systems

The code system, SEMER, was recently developed to evaluate the economic impact of various nuclear reactors and associated innovations. Models for nearly all fossil energy-based systems were also included to provide a basis for cost comparisons.Essentially, SEMER includes three types of model libraries: the global model, for a rapid estimation of various nuclear and fossil energy-based systems, the detailed models, for the finer cost evaluation of individual components and circuits in a PWR type of reactor and the fuel cycle models, for PWRS, HTRs and FBRs, allowing the cost estimations related to all the steps in the nuclear fuel cycle, including reprocessing and disposal.This paper summarises our on-going investigations on new developments in, and on the validation of, the SEMER system.Details of the modelling principles, and the results of validation carried out in the context of an EDF/CEA Joint Protocol Agreement, are also presented.First results of this validation are highly encouraging:

• Relative errors for the total kWh or overnight and investment costs are less than 5% for large PWR systems operating in France or other countries.

• These errors are less than 3% for small-sized compact PWRs and they are of the order of 4–7% for HTRs (as compared to IAEA estimations).

• For fossil energy-based power plants, the relative error, even with slightly different cost breakdown between SEMER and that of existing installations, is from 5 to 20%.

• Similarly, errors on the nuclear fuel cycle costs are about 1–4%, compared to published reference values.

Manufacturing of ultra-large diameter 20 MnMoNi 5 5 steel forgings for reactor pressure vessels and their properties

As the structural material for RPV typical of increased dimensions, a set of ultra-large diameter steel forgings for a PHWR RPV is presented as outlined below.

1. (1) Material designation: 20 MnMoNi 5 5 (similar to SA508, Cl.3)

2. (2) Size of the forgings: flanges, 8.440 mm OD, a weight of 238 tons for shell flange; shells and torus, 7,920 mm OD, with large height; cover dome, 6,800 mm OD in chord and 460 mm thick; blank before formed to dome is ca. 8,000 mm OD.

3. (3) Chemical composition: particular effort was made for minimizing the tramp elements as P, S, As, Sn, Sb, Cu.

4. (4) Manufacturing, key points: steel making - combined refining and degassing in ladle; ingot making - largest size ingots, including 570 ton and 500 ton ingots; forging - special “outside-the-press” forging and forming techniques; heat treatment - prevention of H₂ flaking in normalizing and tempering and handling of the extra-large forgings at water quenching.

5. (5) Metallurgical properties: sufficiently uniform carbon distributions in the forgings; a lowest possible content of hydrogen, non-metallic inclusions and oxygen.

Mechanical properties: uniformity in tensile and toughness properties; flaws - only limited number of spots of UT indications under 2 mm EFG (EFS).     

Analysis of equations of motion with complex stiffness mode superposition method applied to systems with many degrees of freedom

According to past experimental studies, the damping effects of a structure may be considered to be structural damping mechanics in the elastic range, the damping factors or logarithmic damping ratios of which are independent of the frequencies of the disturbing force or the eigenvalues of the structure. In this paper, the authors propose a simple method of expressing the above-mentioned damping effects using complex numbers, although viscous damping mechanics is generally used as the conventional mathematical method. Thus, the spring constant can be expressed as k = k₀ exp(i sgn ωø), where sgn ω = 1 for ω > 0; sgn ω = 0 for ω = 0; sgn ω = −1 for ω < 0.The concept of complex damping is described comparing it with the most common ‘Voigt model’ for a system with a single degree of freedom and it is concluded that both solutions are exactly identical under the conditions of free and forced vibration when both systems have equivalent natural periods and damping ratios. Furthermore, the authors attempt to apply the above complex stiffness to multi systems with many degrees of freedom and investigate their mathematical and dynamical characteristics. The fundamental mathematical characteristics can be described as follows:

1. (1) Any n degrees of freedom system that has 2n distinct eigenvalues occurring as n complex conjugate pairs and n complex conjugate pairs of corresponding eigenvectors according to the definition of ‘sgn ω’.

2. (2) The eigenvectors establish the orthogonality of the frequency domain when either ω > 0 or ω < 0, but they do not establish this property over the domains for both ω > 0 and ω <.

3. (3) By using the above properties, the equations of motion can be reduced to n conjugate pairs of first order differential equations and the solution is obtained by the superposition of n complex conjugate pairs.

The fundamental dynamic characteristics can also be described as follows:

1. (1) When the same damping values are assigned to all structural elements making up a vibrational system, the reduced equations form an estimate of the constant damping ratio over all of the modes from the lowest to the highest.

2. (2) Furthermore, when the different damping values are assigned to each individual structural element, the damping values of the reduced equations denote the value which is equivalent to that of any structure of which the mode shapes are predominant.

Finally, the authors present the computed results of a system with 18 degrees of freedom consisting of four individual structural elements with different damping values. Through the above studies, it is concluded that the authors' method is reasonable for estimating the damping effects of the structure.     

Characteristics of corium debris bed generated in large-scale fuel-coolant interaction experiments

The formation of corium debris as the result of fuel-coolant interaction (energetic or not) has been studied experimentally in the FARO and KROTOS facilities operated at JRC-Ispra between 1991 and 1999. Experiments were performed with 3–177 kg of UO₂–ZrO₂ and UO₂–ZrO₂–Zr melts, quenched in water at depth between 1 and 2 m, and pressure between 0.1 and 5.0 MPa. The effect of various parameters such as melt composition, system pressure, water depth and subcooling on the quenching processes, debris characteristics and thermal load on bottom head were investigated, thus, giving a large palette of data for realistic reactor situations.Available data related to debris coolability aspects in particular are:

• Geometrical configuration of the collected debris.

• Partition between loose and agglomerated (“cake”) debris.

• Particle size distribution with and without energetic interaction.

These data are synthesised in the present contribution.     

FARST — A computer code for the evaluation of FBR fuel rod behavior under steady-state/transient conditions

FARST, a computer code for the evaluation of fuel rod thermal and mechanical behavior under steady-state/transient conditions has been developed. The code characteristics are summarized as follows:

1. (i) FARST evaluates the fuel rod behavior under the transient conditions. The code analyzes thermal and mechanical phenomena within a fuel rod, taking into account the temperature change in coolant surrounding the fuel rod.

2. (ii) Permanent strains such as plastic, creep and swelling strains as well as thermoelastic deformations can be analyzed by using the strain increment method.

3. (iii) Axial force and contact pressure which act on the fuel stack and cladding are analyzed based on the stick/slip conditions.

4. (iv) FARST used a pellet swelling model which depends on the contact pressure between pellet and cladding, and an empirical pellet relocation model, designated as “jump relocation model”.

The code was successfully applied to analyses of the fuel rod irradiation data from pulse reactor for nuclear safety research in Cadarache (CABRI) and pulse reactor for nuclear safety research in Japan Atomic Energy Research Institute (NSRR).The code was further applied to stress analysis of a 1000 MW class large FBR plant fuel rod during transient conditions. The steady-state model which was used so far gave the conservative results for cladding stress during overpower transient, but underestimated the results for cladding stress during a rapid temperature decrease of coolant.     

Analysis of aircraft impact to concrete structures

Analysis of aircraft impact to nuclear power plant structures is discussed utilizing a simplified model of a “fictitious nuclear building” to perform analyses using LS-DYNA software, representing the loading: (i) by the Riera force history method and (ii) by modeling the crash by impacting a model of a plane similar to Boeing 747-400 to the structure (i.e., “missile–target interaction method”). Points discussed include: (1) comparison of shock loading within the building as obtained from the Riera force history analysis versus from the missile–target interaction analysis, (2) sensitivity of the results on the assumed Riera force loading area, (3) linear versus nonlinear modeling and (4) on failure criteria.     

A two-dimensional model for fluid-structure interaction in curved pipes

A “channel” model was developed for the purpose of simulating the interactive fluid-structural response of curved pipes to pressure pulses. Simulation is shown to have been achieved analytically in both the axisymmetric (“breathing”) and transverse (“bending”) modes of interactive behavior.An experimental program which was aimed at the validation of the model is also described. Tests were run in both straight and curved pipe configurations. Comparisons between measurements and model calculations demonstrate the validity of the model within the range of parameters under consideration.The model was implemented into the DISCO code for nonlinear fluid-shell interaction.