An approximate method for calculating the temperature distribution in gas-filled cracked fuel elements

Treating radial cracks by an idealized geometry in fuel elements containing a thermal source gradient, the temperature distribution throughout a cracked fuel element, its gaseous bonding gap, and its surrounding can is found by an approximate series expansion method. This approximation allows the cracked fuel zone to be described by a single series expansion rather than by a multizone approach and allows approximate satisfaction of the boundary conditions at the interfaces of the cracked fuel zone and both at the non-cracked fuel zone and at the can. The method allows for the temperature dependence of the fuel and that of the gas mixture in the cracks and bonding gap, and takes into account the effect of crack openings on gap conductance at the fuel-can interface. The temperature distribution, its mean and variance resulting from the stochastic distribution of radial crack locations, are found. The case of hairline radial cracks, the mean locations of which are azimuthally uniformly distributed, is used to illustrate the importance of cracks on the can temperature distribution and it is shown that their presence may lead to central fuel zone melting problems.     

An evaluation of approximate methods for calculating anisotropic flux escape and transmission probabilities for cylindrical annular regions

In the interface current method for solving the integral transport equation, most of the computer time is spent in the precalculation of various region transmission, escape and collision probabilities. Therefore, any reduction in computer time used to calculate these probabilities will directly affect the efficiency of this method. The normal methods such as the Trapezoidal rule or Gauss-quadrature formula for calculating the various probabilities require the evaluation of many Bickley functions per integral, which is time consuming. This paper discusses efficient methods for calculating the various probabilities corresponding to anisotropic terms of the angular flux expansion at region interfaces for cylindrical annular geometry. The paper first discusses the application of Bonalumi's Pseudo-Linear (P-L) approximation and the second-order correction to it which requires the evaluation of one and two Bickley functions, respectively, per integral. The accuracy of the second-order approximation is of the order of 0.1% for all the probabilities except the transmission probability from outer to outer surface (P_ρv∞) of the region (where ρ and v denote the order of anisotropy of the flux entering and leaving the outer boundary of the annular region). The paper then discusses a Gauss-quadrature formula with exponential weighting and its modified form which is suitable for calculating P^ρv_∞ efficiently.     

An efficient method for calculating diffusive flow to a spherical boundary

The problem of diffusive flow to a spherical boundary is approximated by describing the concentrations of the diffusing species in terms of quadratic functions in two concentric regions. A variational principle is used to calculate the radial distribution of concentration. This approach forms the basis of a rapid and economic algorithm for computing gas release in fuel behaviour codes. By this means better accuracy and faster running times are obtained than using the finite-difference method and the difficulties associated with using the Booth approximation when irradiation conditions change are overcome.     

A numerical method for predicting seismic-induced impact between subassemblies in LMFBR cores

Structural problems that incorporate impact usually require small time steps for numerical integration and, consequently, solutions are very expensive. Since impact is one of the basic phenomena involved in any study of fast breeder reactor cores subjected to seismic disturbances, it is imperative that simplified models be introduced to make safety studies economically feasible. An approach is proposed in this paper whereby just the magnitude of each impulse and not the history of the impact force is determined for each impact. The consequence of the procedure is that the maximum time step is governed by system parameters and not by a detailed characteristic of the contact region such as an equivalent contact spring. The concepts are developed with the use of a single-degree-of-freedom model and the approach is applied to a three-assembly model of a reactor core. To obtain a solution, it is shown that the proposed direct approach may result in computer time that is less by an order of magnitude then the time required by the more conventional contact spring and gap element method.     

On the potential for plugged core pressurization following a hypothetical accident in an LMFBR

Steady state and transient conditions for a two-phase liquid-vapor cylindrical UO₂ pool are analytically investigated. The analysis relies on extrapolation of experimental results from internally heated boiling simulant fluid pools. The internal heat generation rates that can sustain a vapor-liquid pool under steady state consitions are calculated. The pressure transients that can be expected in the event of an imbalance between heat generation rate and heat removal rate are also calculated. The analysis presented demonstrates the significance of accounting for heat removal from the pool for proper assessment of its pressurization potential.     

An approximate method for computation of probability intervals for the top-event probability of fault trees

This paper proposes a procedure for obtaining the probability intervals for the top-event probability of a fault tree by exploiting an empirical linear relationship between the logarithm of the top-event probability and the logarithms of the basic event probabilities. The procedure is computationally fast, and several examples indicate that they yield reasonably accurate results.     

核临界事故报警系统布置分析方法研究

本文阐述了布置核临界事故报警系统的意义和原则,分析了核临界事故可能发生的机理,初步建立了一套核临界事故情景假设分析方法。研究了最小临界事故源项计算方法以及三维剂量场分布计数的方法,采用各设备最小临界事故剂量场分布最小值等高线图的方法来从众多剂量场分布图中优化选取合适的核临界事故报警系统布置点位,以确保其可以覆盖到每个具有核临界事故风险的设备,并对核临界事故报警系统探头类型选择的原则和方法进行了分析。     

An approximate method for solving radiation and neutron transport problems in spatially stochastic media

A new approach has been developed to deal with stochastic transport problems in three-dimensional media. This is done by assuming, a priori, a functional form for the stochastic flux in terms of the members of a random set function. For the case of a two-phase medium, two coupled integro-differential equations are obtained for the deterministic functions that arise and expressions are given for the mean and variance of the angular flux. There is a close relationship between these equations and those of the Levermore–Pomraning (LP) theory, but they offer an opportunity to deal with more general forms of stochastic processes. It is also shown that the coupling coefficient between the phase equations is directly proportional to the gradient of the autocorrelation function evaluated at the origin; a feature which has been noted in other fields in which random media occur. By making plausible assumptions about the functional form of the autocorrelation function, different forms of the transport equations can be obtained, according to the structure of the medium. For the one-dimensional case, we may show an exact correspondence with the LP equations. Discussions are given regarding the application of the method to three-dimensional problems for which we expect it to be a good approximation for the mean. We also note that the equations are applicable to realistic problems, such as grains embedded in a background matrix, and not restricted to slabs. Investigations into the variance have also been made and a simple approximation scheme developed which gives reasonable agreement with the simulation results of Adams et al. [Adams, M.L., Larsen, E.W., Pomraning, G.C., 1989. Benchmark results for particle transport in a binary Markov statistical medium. Journal of Quantitative Spectroscopy & Radiative Transfer, 42, 253].     

An analysis of containment failure by a steam explosion following a postulated core meltdown in a light water reactor

The Reactor Safety Study (WASH-1400) assessed the probability of containment failure via a steam explosion during a postulated core meltdown accident to be 10⁻². Large uncertainties were attached to this probability and research has continued to reduce the uncertainty.In this paper, we discuss the possible consequences of a steam explosion for a specific reactor system (Zion Nuclear Station—Pressurized Water Reactor). It is our opinion, based on the analysis performed, that generation of large mass missiles by the explosion is unlikely, while small mass missiles, although more likely would not pose a threat to the containment. We do not mean to imply that steam explosions can be disregarded during a postulated meltdown accident, but rather that emphasis should now be placed on how the explosion affects the overall core meltdown accident instead of causing a direct failure.     

A method for calculating proton-nucleus elastic cross-sections

Recently [Nucl. Instr. and Meth. B 145 (1998) 277; Extraction of in-medium nucleon-nucleon amplitude from experiment, NASA-TP, 1998], we developed a method of extracting nucleon-nucleon (N-N) cross-sections in the medium directly from experiment. The in-medium N-N cross-sections form the basic ingredients of several heavy-ion scattering approaches including the coupled-channel approach developed at the NASA Langley Research Center. We investigated [Proton-nucleus total cross-sections in coupled-channel approach, NASA/TP, 2000; Nucl. Instr. and Meth. B 173-174 (2001) 391] the ratio of real to imaginary part of the two body scattering amplitude in the medium. These ratios are used in combination with the in-medium N-N cross-sections to calculate proton-nucleus elastic cross-sections. The agreement is excellent with the available experimental data. These cross-sections are needed for the radiation risk assessment of space missions.     

An efficient parallel computing scheme for Monte Carlo criticality calculations

The existing parallel computing schemes for Monte Carlo criticality calculations suffer from a low efficiency when applied on many processors. We suggest a new fission matrix based scheme for efficient parallel computing. The results are derived from the fission matrix that is combined from all parallel simulations. The scheme allows for a practically ideal parallel scaling as no communication among the parallel simulations is required, and inactive cycles are not needed.     

The criticality problems with the FN method for the FBIS model

In one-speed, time-independent, neutron transport theory, the F_N method is used for the FBIS (forward-backward-isotropic scattering) model to reinvestigate the behaviour of the critical size in plane and spherical geometries. For the FIS (forward-isotropic scattering) model the numerical results are compared with previously obtained variational results and it is shown that they are in agreement. For the BIS (backward-isotropic scattering) model exact results are obtained and compared with the first-order approximate results obtained using the method of elementary solutions.     

A method for solving a stochastic eigenvalue problem applied to criticality

We present a novel approach to calculate stochastic eigenvalues of differential and integral equations using polynomial chaos theory. The method is applied to a criticality problem using the diffusion equation. This technique has the advantage of avoiding the non-linear terms in the conventional method of stochastic eigenvalue calculation but it does require an additional, ‘pseudo-time’, independent variable t.