Enhanced computer reliability for nuclear power applications

Reactor operator assistance and augmentation by on-line digital computers will improve power reactor safety. To function in this expanded role, the computers must be both extremely reliable and failsafe. Topics in computer and software reliability are discussed, and it is pointed out that all of these error-extinguishing characteristics are available today in general-purpose equipment built for the military. Tactical military computers, peripheral equipment, and high-order languages have the refinements necessary for safety-related reactor control room operations.     

On the structural reliability of reactor safety containments

A method for reliability based design of reactor safety containments is suggested, and a brief review of classical reliability analysis is presented. Seismic and climatic load occurrences are modeled by uniform Poisson processes. Extreme value distributions are assumed to represent the seismic, climatic, external and internal pressure load intensities. Reliabilities are calculated for various design loads and load combinations.     

The karlsruhe computer program for the evaluation of the availability and reliability of complex repairable systems

A very fast analytical computer program for fault tree evaluation has already been developed at the german nuclear research center of Karlsruhe. This program can solve coherent systems in binary logic. Four different classes of components can be handled by the program

1. 1. Unrepairable components

2. 2. Repairable components with failures which are immediately detected (revealed faults)

3. 3. Repairable components with failures which are detected upon demand (faults remain unrevealed until next demand occurs)

4. 4. Repairable components with failures which are detected upon inspection (faults remain unrevealed until next inspection is carried out).

The program can perform also time dependent calculations. In particular the program can analyse systems characterized by two phases one following the other in time (two time axis). A numerical example is also included.     

On the theoretical-numerical study of the HEXCALIBER mock-up thermo-mechanical behaviour

Within the framework of the R&D activities promoted by European Fusion Development Agreement on the Helium-Cooled Pebble Bed Test Blanket Module to be irradiated in ITER, ENEA Brasimone and the Department of Nuclear Engineering of the University of Palermo (DIN) performed intense research activities on the modelling of the thermo-mechanical behaviour of both beryllium and lithiated ceramics pebble beds, that are envisaged to be used, respectively, as neutron multiplier and tritium breeder. In particular, the DIN developed a thermo-mechanical constitutive model for these pebble beds to be validated against the HEXCALIBER mock-up test campaign, carried out at the ENEA HE-FUS3 facility.The paper presents the main results of the mock-up experimental tests and of their numerical simulations performed adopting the finite element method, which allowed the DIN constitutive model to be assessed and validated.     

On the incorporation of damping in large, general-purpose computer programs

Damping plays an important role in the dynamic response of structures and equipment subjected to broadband excitation such as that due to earthquake. Its incorporation into general-purpose shock and vibration computer programs has been based on either a concern for the physical mechanisms of damping or on the need for mathematical convenience. The more physical approach starts with the equation of motion

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, where [C], the damping matrix, is derived from element properties in a manner consistent with the derivation of [K]. Expressions for a consistent damping matrix exist for radiation of energy by travelling waves, fluid flow damping and internal energy dissipation by the material. Under certain conditions, it is convenient to incorporate the material damping as a complex stiffness, i.e.

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. The equation of motion can then be rewritten in a symmetric form. The equations can be uncoupled by the damped, complex eigenvalues and solved by modal superposition.An alternative approach, which is mathematicall more convenient, is to choose a form for [C] which is reduced to diagonal form by the undamped, real eigenvalues associated with the equation of motion

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. Two common choices for such a damping matrix are the generalization of proportional damping suggested by Caughey and the selection of equivalent viscous modal damping coefficients using the strain energy weighting technique suggested by Biggs. Both these choices for the form of [C] are conducive to solution by modal superposition; however, some mention will be made of the role of damping in solutions which use direct integration or frequency domain techniques.     

On the multiaxial behaviour of concrete exposed to high temperature

An attempt is made to formulate a multiaxial constitutive model for concrete in the temperature range up to 800°C. The proposed model can be characterized as isotropic, elastic-viscoplastic-plastic in the compression region. Brittle failure is assumed in the tensile region.The thermal strain increment is assumed to be a function of both temperature and the current stress tensor. This assumption implies that the thermal strain may have deviatoric components.The volumetric thermal strain is used as a scalar damage measure instead of temperature itself. The corresponding softening function is obtained from isothermal, uniaxial tests. Also the elastic properties are taken as functions of the volumetric thermal strain.The response of the model is illustrated and compared with experimental results.     

On the implication of systems and structural reliability analyses in nuclear safety

The intention of this paper is to discuss some aspects of applicability and of actual application of both systems and structural reliability analyses, rather than to elaborate on basic methodical problems. The point of view is not that of a theorist or an analyst, but that of a user of results, gained by whatever effective tools.     

On modelling of kinematic hardening for ratcheting behaviour

A kinematic hardening rule is formulated on the assumption that each component α_i of back stress has a critical state for its dynamic recovery to be fully activated. The rule has a feature that only the projection of plastic strain rate to the direction of α_i contributes to the dynamic recovery. This is in contrast with previous rules in which the accumulated plastic strain rate enters into the dynamic recovery term. Applying the present and previous rules to experiments of modified 9Cr-1Mo steel at 550°C, we discuss effects of the feature mentioned above on simulating the multiaxial as well as uniaxial ratcheting behaviour.     

Use of structurally imperfect crystals to bind elements of technogenic geomechanical media

A. P. Vinogradov Institute of Chemistry and Geochemistry, Siberian Branch, Russian Academy of Sciences. Translated from Atomnaya Énergiya, Vol. 72, No. 3, pp. 251–255, March, 1992.     

On mathematical models for calculating the mechanical behaviour of coated fuel particles

Coated fuel particles, as used in high-temperature gas-cooled reactors, consist of a fuel kernel and a spherically symmetric multilayer coating. During their lifetime they undergo varying stress states, caused by the simultaneous occurrence of a number of basic physical effects.     

On the rate theory model for fission-gas behaviour in nuclear fuels

The rate theory model of the homogeneous nucleation and subsequent growth of intragranular fission gas bubbles has been extended to allow for the inclusion of very much larger bubbles. A simple treatment of the behaviour of grain-boundary gas is included in the present model, which allows for the re-solution of gas from intergranular bubbles. The effect of varying the model parameters and of including bubble mobility in the theory have been considered and it is concluded that the dominant parameters for gas release are temperature, grain size, re-solution rate and bubble migration and coalescence.     

On the analogies in the dynamic behaviour of heated channels with boiling and supercritical fluids

In this paper, the origin and the consequences of a new dimensionless formalism recently introduced for analysing the dynamic behaviour of heated channels with fluids at supercritical pressures are discussed. A unified view of boiling and supercritical fluid instabilities is proposed, basing on the argument that, despite the strong differences in their operating conditions, in both cases the relevant dynamics results from the changes in density that the fluid undergoes along the channel.The discussion is presently supported only by modelling, performed both by a simplified program and a system code; however, considering the complete independence of these modelling tools, the close agreement observed between their results provides a reasonable level of confidence in the proposed conclusions.Interesting thermodynamic relationships, devised as a by-product of the introduction of the new dimensionless parameters, are also presented, in the aim to stimulate further studies capable to provide greater insight into the fascinating aspects raised by recognising the intimate similarity of these two classes of phenomena, which have such a remarkable relevance for present and future nuclear reactor technology.     

On behaviour of fuel elements subject to combined cyclic thermomechanical loads

This paper presents detailed finite element formulations on the kinematic hardening rule of plasticity included in an existing thermoelastoplastic stress analysis code primarily designed to predict the thermomechanical behaviour of nuclear reactor fuel elements. The kinematic hardening rule is considered to be important for structures subject to repeated (or cyclic) loads. The start-up/operation/shut-down and various power excursions in a reactor all can be classified as cyclic loadings. In addition to the shifting of material yield surfaces as usually handled by the kinematic hardening rule, the thermal effect and temperature-dependent material properties have also been included in the present work for the first time.A case study related to an in-reactor experiment on a single fuel element indicated that significantly higher cumulative sheath residual strains after two load cycles was obtained by the present scheme than those calculated by the usual isotropic hardening rule. This observation may alert fuel modellers to select proper hardening rules in their analyses.     

A comparison of predictions of high-temperature steam properties

Recent literature pertaining to high temperature steam properties has been assessed. After careful assessment of available sets of property tables and equations for high temperature (including dissociated) steam, a set of high temperature steam properties was selected, based heavily on Vargaftik steam tables. A computer code, UODH2O (University of Ottawa Dissociated H₂O code) is constructed to compute high-temperature steam properties using a lookup table and interpretation technique. The code, which required input values of pressure (0.01–100.0 MPa) and temperature (1000–5726.85°C), can predict four thermodynamic properties - specific volume, entropy, enthalpy and heat capacity, and two transport properties - viscosity and thermal conductivity.     

The effect of turbulent mixing models on the predictions of subchannel codes

In this paper, the predictions of the COBRA-IV and ASSERT-4 subchannel codes have been compared with experimental data on void fraction, mass flow rate, and pressure drop obtained for two interconnected subchannels. COBRA-IV is based on a one-dimensional separated flow model with the turbulent intersubchannel mixing formulated as an extension of the single-phase mixing model, i.e. fluctuating equal mass exchange. ASSERT-4 is based on a drift flux model with the turbulent mixing modelled by assuming an exchange of equal volumes with different densities thus allowing a net fluctuating transverse mass flux from one subchannel to the other. This feature is implemented in the constitutive relationship for the relative velocity required by the conservation equations. It is observed that the predictions of ASSERT-4 follow the experimental trends better than COBRA-IV; therefore the approach of equal volume exchange constitutes an improvement over that of the equal mass exchange.     

Validation of the MCNP5 computer code

The MCNP5 computer code with the ENDF/B6 neutron data library is validated for problems which are of current importance at the Russian Federal Nuclear Center — All-Russia Research Institute of Technical Physics. Comparative calculations performed with the MCNP5 code and its preceding version MCNP4c are identical within the limits of computational error. This confirms that the MCNP5 code can be used instead of the previous versions. __________ Translated from Atomnaya énergiya, Vol. 101, No. 2, pp. 112–116, August, 2006.