A simple model for straggling evaluation

Some straggling models had largely been abandoned in favor of Monte Carlo simulations of straggling which are accurate but time consuming, limiting their application in practice. The difficulty of simple analytic models is the failure to give accurate values past 85% of the particle range. A simple model is derived herein based on a second order approximation upon which rapid analysis tools are developed for improved understanding of material charged particle transmission properties.     

A simple model for integral hadron-nucleus and nucleus-nucleus cross-sections

A model for hadron-nucleus and nucleus-nucleus cross-sections based on simplified Glauber approach is proposed. The predictions of the model are compared with experimental data for the inelastic and the total hadron-nucleus and inelastic nucleus-nucleus cross-sections from available databases.     

A simple representation for the angular dependence of scattered and recoil particle energies

A simple graphical method is presented which depicts the velocity-angle dependence of binary collisions by circles on a polar plot. This method works not only for elastic collisions but also for inelastic collisions and for multiple scattering events. It is an especially useful aid for visualizing energy-angle relationships for scattered and recoil particles.     

Elastic-plastic analysis of small cracks in tubes under internal pressure and bending

Elastic-plastic finite element analyses were conducted to generate new solutions of J-integral and crack-opening displacement (COD) for short through-wall cracks in pipes subjected to combined bending and tension loads. The results are presented in terms of the well-known GE/EPRI influence functions to allow comparisons with some limited results in the literature. Two different pipe pressures with values of 7.24 MPa (1050 psi) and 15.51 MPa (2250 psi) simulating BWR and PWR operating conditions, respectively, were used to evaluate the effects of pressure on J and COD. Pipes with various radius-to-thickness ratios, crack sizes, and material parameters were analyzed. Limited analyses were also performed to evaluate the effects of hoop stresses in pipes under pure pressure loads. The results suggest that the fracture response parameters can be significantly increased by pressure-induced axial tension for larger crack size, material hardening constant, and radius-to-thickness ratio of the pipe. The presence of pressure-induced hoop stresses also increases the fracture response, but in low-hardening materials their effects are insignificant due to small plastic-zone size that was expected for the intensity of pipe pressure and crack size considered in this study. However, for high-hardening materials when the plastic-zone size is not negligible, the hoop stresses can moderately increase J and COD.     

Coalescence evaluation of collinear axial through-wall cracks in steam generator tubes

To maintain the structural integrity of steam generator tubes, usually, 40% of wall thickness plugging criterion has been adopted. However, since the criterion is applicable only for the steam generator tube containing a single crack, the interaction effect of multiple cracks cannot be considered. In this paper, the coalescence pressure of tube with dual cracks is evaluated based on detailed three-dimensional elastic–plastic finite element analyses. In terms of the crack configuration, collinear axial through-wall cracks with various length, distance and ratio between individual cracks are selected. The applicability of failure pressure prediction models recently proposed by the authors was verified by comparing the finite element analyses results with corresponding experimental data for tubes with two identical cracks. Further, in order to quantify the effect of crack length ratio on failure behavior, the failure pressure prediction model was used expansively for tubes containing different-sized cracks and a coalescence evaluation diagram was developed.     

A high-temperature creep model for Zr-2.5 wt% Nb pressure tubes

For a postulated loss-of-coolant accident in a CANDU reactor, in which the primary cooling circuit fails to remove the heat generated in the core, the temperature of the pressure tubes could rise very quickly. Since any deformation of the pressure tubes would control how the core heat is transferred to the surrounding moderator, which is a large heat sink, the accurate prediction of this transient deformation is essential. The majority of the pressure tubes in CANDU reactors are cold-worked Zr-2.5 wt% Nb and creep equations for this material have been developed from uniaxial creep tests. These creep equations were successful in predicting the creep strain in constant-stress uniaxial tests in which the temperature was ramped at rates ranging from 1° C/s to 50° C/s. They also successfully predicted the ballooning of internally pressurized sections of pressure tube that were heated at about 5° C/s.     

A CFD model for particle dispersion in turbulent boundary layer flows

In Lagrangian particle dispersion modeling, the assumption that turbulence is isotropic everywhere yields erroneous predictions of particle deposition rates on walls, even in simple geometries. In this investigation, the stochastic particle tracking model in Fluent 6.2 is modified to include a better treatment of particle–turbulence interactions close to walls where anisotropic effects are significant. The fluid rms velocities in the boundary layer are computed using fits of DNS data obtained in channel flow. The new model is tested against correlations for particle removal rates in turbulent pipe flow and 90° bends. Comparison with experimental data is much better than with the default model. The model is also assessed against data of particle removal in the human mouth–throat geometry where the flow is decidedly three-dimensional. Here, the agreement with the data is reasonable, especially in view of the fact that the DNS fits used are those of channel flows, for lack of better alternatives. The CFD Best Practice Guidelines are followed to a large extent, in particular by using multiple grid resolutions and at least second order discretization schemes.     

A simple method for measuring the moments of the gamma particle multiplicity distribution

In this paper we propose an efficient statistical method for estimating the moments of the secondary γ multiplicity distribution in high energy bubble chamber processes. Our method requires relatively small statistics, even if the detection losses are considerable, as is demonstrated by calculating the dispersion of the secondary π° multiplicity distribution from 1200 events with a detection probability of about 25% for γ's.     

A simple novel and fast computational model for the LIVE-L4

The LIVE-L4 test was conducted to investigate the transient and steady state behavior of the molten pool and the crust influenced by different heat generation rates. The main purpose of this work is to develop a simple novel model of the LIVE code to calculate the entire process of the LIVE-L4 test after the melt of KNO₃–NaNO₃ poured into the test vessel. The LIVE code is a transient code and can be used as a fast computational program to calculate the LIVE tests. Natural convection heat transfer in the melt pool, crust behavior, heat conduction in the vessel wall, and radiative heat transfer were all considered in the model of the LIVE code.In the LIVE code, Asfia–Dhir correlations were used to calculate average and local heat transfer coefficients in the melt pool. With the assumption of no considering the composition change of local melt at melt/crust interface, many important parameters, including the melt pool temperature, heat flux distribution along the vessel wall, the thickness of the crust in steady state, and crust growth rate during the test, were calculated and compared with the LIVE-L4 experimental data.The melt pool Nu calculated by the LIVE code is larger than experimental data due to the use of Asfia–Dhir correlation in the LIVE code, which caused the average heat flux through the vessel wall larger than experiment data except the heating phase of 5 kW. It is attributed that the temperature difference between the melt pool temperature and the interface temperature at melt/crust measured in the test is larger than that calculated by the LIVE code due to the constant interface temperature at melt/crust of 284 °C used in the LIVE code. Crust growth rate calculated by the LIVE code was consistent well with the experiment data. Calculation results indicated that the LIVE code could generally predict the main parameters of the melt and crust well during the LIVE-L4 test.     

A mechanistic critical heat flux model for wide range of subcooled and low quality flow boiling

A mechanistic model to predict a critical heat flux (CHF) over a wide operating range in the subcooled and low quality flow boiling has been proposed based on a concept of the bubble coalescence in the wall bubbly layer. The conservation equations of mass, energy and momentum, together with appropriate constitutive relations, are solved analytically to derive the CHF formula. The model is characterized by an introduction of the drag force due to wall-attached bubbles roughness in the momentum balance, which determines the limiting transverse interchange of mass flux crossing the interface of the wall bubbly layer and core. Comparison between the predictions by the proposed model and the experimental CHF data shows good agreement over a wide range of parameters for both light water and fusion reactors operating conditions. The model correctly accounts for the effects of flow variables such as pressure, mass flux and inlet subcooling as well as geometry parameters.     

A new empirical model for self-leveling behavior of cylindrical particle beds

ABSTRACT

During the material relocation phase of core disruptive accidents in sodium-cooled fast reactors, the rapid quenching and fragmentation of molten materials discharged from the reactor core into the lower plenum region can lead to the formation of debris beds. Coolant boiling may lead to leveling of the mound-shaped beds, which changes both the beds' coolability with decay heat in the fuel and the neutronic characteristics. In this study, a series of experiments using simulant materials were performed to develop an experimental database of self-leveling processes of particle beds in a cylindrical system. To simulate the coolant boiling in the beds in the experiments, a gas injection method was used to percolate nitrogen gas uniformly through the base of a bed with a conical-shaped mound. Time variations in bed height during the self-leveling process were measured for different particle sizes, densities and sphericities, and gas injection velocities. Using a dimensional analysis approach, a new model was proposed. This model correlates the experimental data on transient bed height with an empirical equation using a characteristic time for self-leveling development and an equilibrium bed height. The proposed model reasonably predicts the self-leveling development of particle beds.     

A simple forced diversion model for study of thermal-hydraulic transients in LMFBR subassembly

The generalized simple, transient, integral energy balances based on the average properties for the fuel and cladding have been used in our new multichannel thermal-hydraulic model for calculating the transient behavior of coolant in the rod bundle. This model was developed to provide a simple useful tool for analyzing the flow and thermal transients in a rod bundle with reasonable accuracy, and to understand the fundamental characteristics of flow in the rod bundle under both normal and abnormal condition of reactor-core operation.     

A simple excursion model of a nuclear explosive device

An analytical model based on basic physics and on a third-order ordinary differential equation is presented to describe the sequence of events during an excursion of a nuclear explosive device. The model is subdivided into two parts: (a) the time span up to the boiling point without any relevant feedback mechanism, and (b) the time span beyond the boiling point where a strong feedback mechanism exists due to the expanding core volume.The model yields reasonable results which were cross-checked repeatedly.     

A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one- and three-dimensional computer codes

Based on a review of visual observations at or near critical heat flux (CHF) under subcooled flow boiling conditions and consideration of CHF triggering mechanisms, presented in a companion paper [Le Corre, J.M., Yao, S.C., Amon, C.H., 2010. Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions. Nucl. Eng. Des.], a model using a two-dimensional transient thermal analysis of the heater undergoing nucleation was developed to mechanistically predict CHF in the case of a bubbly flow regime. The model simulates the spatial and temporal heater temperature variations during nucleation at the wall, accounting for the stochastic nature of the boiling phenomena. It is postulated that a high local wall superheat occurring underneath a nucleating bubble at the time of bubble departure can prevent wall rewetting at CHF (Leidenfrost effect). The model has also the potential to evaluate the post-DNB heater temperature up to the point of heater melting.Validation of the proposed model was performed using detailed measured wall boiling parameters near CHF, thereby bypassing most needed constitutive relations. It was found that under limiting nucleation conditions; a peak wall temperature at the time of bubble departure can be reached at CHF preventing wall cooling by quenching. The simulations show that the resulting dry patch can survive the surrounding quenching events, preventing further nucleation and leading to a fast heater temperature increase. The model was applied at CHF conditions in simple geometry coupled with one-dimensional and three-dimensional (CFD) codes. It was found that, within the range where CHF occurs under bubbly flow conditions (as defined in Le Corre et al., 2010), the local wall superheat underneath nucleating bubbles is predicted to reach the Leidenfrost temperature. However, a better knowledge of statistical variations in wall boiling parameters would be necessary to correctly capture the CHF trends with mass flux (or Weber number).     

A fractionation model based on three lognormal particle size distributions

In this paper, a new model is proposed to calculate distribution of fission products in particles of different sizes. The model sensitivity to the effective volume and mass of vaporized soil particles is examined. Compared with other fractionation models, the new method has a much better performance in calculating r89,95, but the calculated cumulative activity fraction for particles in diameters over 100 μm is in between the results using the F-T and G-X models. It is concluded that in a near surface nuclear explosion radioactivity is mainly distributed in soil particles which have not been vaporized, and according to the Henry's law and ideal gas law, r89,95 may vary in larger particles when effective volume of the fireball is changed.