Delayed Neutron Precursors Research Articles

Nodal neutron kinetics model based on nonlinear iteration procedure for LWR analysis

A 3-dimensional neuron kinetics model based on the analytical nodal method and nonlinear iteration procedure is developed for Light Water Reactor (LWR) transient calculations. The solution procedure is decoupled on a local solution of the nodal equations for two-node problems and global iterations of the coarse-mesh finite-difference method. An orthogonality of the basic functions used for the neutron flux expansion results in an efficient algorith of the solution of the nodal equations for the two-node problem. The initial system of 8 G nodal equations is reduced to a set of G and 2 G equations, where G is a number of neutron energy groups. A fully implicit scheme with an analytical treatment of the delayed neutron precursors equations is used for time integration. An adaptive time-step size control procedure based on the time-step doubling technique is applied. The described numerical methods are implemented into the computer code SKETCH-N. The 3D LWR Langenbuch-Maures Werner (LMW) operational transient and 2D and 3D Boiling Water Reactor (BWR) LRA super-prompt-critical benchmark problems are calculated in order to verify the code. A comparison of the computed results with the solutions obtained by the other nodal computer codes demostrate fidelity and efficiency of the SKETCH-N code.

98/02141 Nodal neutron kinetics model based on nonlinear iteration procedure for LWR analysis

A 3-dimensional neuron kinetics model based on the analytical nodal method and nonlinear iteration procedure is developed for Light Water Reactor (LWR) transient calculations. The solution procedure is decoupled on a local solution of the nodal equations for two-node problems and global iterations of the coarse-mesh finite-difference method. An orthogonality of the basic functions used for the neutron flux expansion results in an efficient algorith of the solution of the nodal equations for the two-node problem. The initial system of 8G nodal equations is reduced to a set of G and 2G equations, where G is a number of neutron energy groups. A fully implicit scheme with an analytical treatment of the delayed neutron precursors equations is used for time integration. An adaptive time-step size control procedure based on the time-step doubling technique is applied. The described numerical methods are implemented into the computer code SKETCH-N. The 3D LWR Langenbuch-Maures Werner (LMW) operational transient and 2D and 3D Boiling Water Reactor (BWR) LRA super-prompt-critical benchmark problems are calculated in order to verify the code. A comparison of the computed results with the solutions obtained by the other nodal computer codes demostrate fidelity and efficiency of the SKETCH-N code.

Evidence of Source Dominance in the Dynamic Behavior of Accelerator-Driven Systems

In a dynamic simulation method recently developed for accelerator-driven subcritical waste transmutation systems, power levels are renormalized dynamically based on the changing reactivity of the flowing system. For such systems, the power varies directly with the source strength, and inversely with the reactivity. The prompt-jump form of the point-kinetics equations has been used to provide the dynamic renormalization factor for the spatially dependent flowing-fuel system. A unique characteristic of the source-dominated system has been discovered. In the traditional reactor system, power changes are controlled by the half-life for decay of the longest-lived delayed neutron precursors. For the source-dominated system, the delayed neutron precursors do not appreciably slow the response of the system.

Development of a Three-Dimensional Core Dynamics Analysis Program for Commercial Boiling Water Reactors

Development and qualification results are described for a three-dimensional, time-domain core dynamics analysis program for commercial boiling water reactors (BWRs). The program allows analysis of the reactor core with a detailed mesh division, which eliminates calculational ambiguity in the nuclear-thermal-hydraulic stability analysis caused by reactor core regional division. During development, emphasis was placed on high calculational speed and large memory size as attained by the latest supercomputer technology.The program consists of six major modules, namely a core neutronics module, a fuel heat conduction/transfer module, a fuel channel thermal-hydraulic module, an upper plenum/separator module, a feedwater/recirculation flow module, and a control system module. Its core neutronics module is based on the modified one-group neutron kinetics equation with the prompt jump approximation and with six delayed neutron precursor groups. The module is used to analyze one fuel bun dle of the reactor core with one mesh (region). The fuel heat conduction/transfer module solves the onedimensional heat conduction equation in the radial direction with ten nodes in the fuel pin. The fuel channel thermal-hydraulic module is based on separated three-equation, two-phase flow equations with the drift flux correlation, and it analyzes one fuel bundle of the reactor core with one channel to evaluate flow redistribution between channels precisely. Thermal margin is evaluated by using the GEXL correlation, for example, in the module.In the upper plenum/separator module, the upper plenum is modeled as a single volume in the thermal-equilibrium state and water spiraling in the separator is modeled by an effective length in the momentum equation. In the feedwater/recirculation flow module, the single-phase flow model is solved with the assumption of incompressive flow. Finally, the control system module includes the recirculation flow control minimodule, the pressure control minimodule, and the feedwater control minimodule, as well as the interlock functions, which work during a transient to allow analysis of general transient phenomena.The program was verified to provide satisfactory results within reasonable computational time based on application analysis of stability and scram phenomena in a BWR-5 type plant.

Delayed neutron effectiveness in a fluidized bed fission reactor

In a fluidized bed of fuel particles suspended by gas a considerable spatial redistribution of delayed neutron precursors occurs due to mixing processes. On the basis of a simple reactor model the reactivity effect of precursor redistribution is analyzed. This analysis is performed for both the limit case of ideal mixing and the general case of finite precursor diffusion length. It is shown that k-infinity and the ratio between precursor diffusion length and neutron diffusion length are the relevant parameters determining the reactivity effect and the effectiveness of the delayed neutrons.

A method to reduce space-time effects in the measurement of reactivities by the rod-drop technique

A method to reduce the dependence on detector location is proposed for the measurement of reactivities of control rods with the rod-drop technique. Values are obtained from data adjustment for the delayed transient, using a function obtained by expansion of the neutronic density into the initial set of kinetic eigenfunctions. The principal hypotheses of the method here proposed, which were verified by experimentations and simulations, are: (1) the contribution of each mode “ q” is the same for every delayed neutron precursor group, (2) the contribution of the higher modes in the delayed population is small compared to that of the fundamental harmonic mode, and (3) for a real control rod insertion, the delayed transient in the adjustment region is similar to an instantaneous one having a delay time. In order to have reasonable experimental errors it is necessary to maintain the fluctuations of the signal within a small value, thus a model was developed to relate the fluctuations with parameters that can be modified in the measuring process. The method was applied in the RA-6 reactor to measure the worth of control rods. It was found that the method can be applied up to 15 dollars and that it does not depend on the relative location of detectors and control rods, as the method based on the point reactor model does.

Development of Computer Code SAFFRON for Evaluating Breached Pin Performance in FBR's

In order to evaluate the breached pin behavior in FBR, the breached pin performance analysis code SAFFRON was developed. Based on the results of run-beyond-cladding-breach test in EBR-II as a collaborative program between PNC and U.S. DOE, the following behaviors were taken into cosideration; fuel sodium reaction product (FSRP) formation, resultant fuel expansion, breach extension of cladding and release of delayed neutron precursors into the coolant. Using 3-dimensional elastic analyses by finite element method, breached pin diameter increase is adequately predicted with the reduced Young's modulus of the breached fuel. The delayed neutron signal response in on-line diagnosis was evaluated in relation to the growth of FSRP and breached area enlargement.

Development of Computer Code SAFFRON for Evaluating Breached Pin Performance in FBR's.

In order to evaluate the breached pin behavior in FBR, the breached pin performance analysis code SAFFRON was developed. Based on the results of run-beyond-cladding-breach test in EBR-II as a collaborative program between PNC and U.S. DOE, the following behaviors were taken into cosideration; fuel sodium reaction product (FSRP) formation, resultant fuel expansion, breach extension of cladding and release of delayed neutron precursors into the coolant. Using 3-dimensional elastic analyses by finite element method, breached pin diameter increase is adequately predicted with the reduced Young's modulus of the breached fuel. The delayed neutron signal response in on-line diagnosis was evaluated in relation to the growth of FSRP and breached area enlargement.

Yields of Delayed Neutron Precursors in the Fission of Actinides

Yields of Delayed Neutron Precursors in the Fission of Actinides

In-Vessel Thermohydraulics Evaluation of an Unprotected Transient Overpower Accident and Delayed Neutron Precursor Concentration Transport Analysis Using a Multidimensional Code

This paper reports on a three-dimensional in-vessel thermohydraulics analysis that is carried out for the early phase of an unprotected transient overpower (UTOP) accident and delayed neutron precursor concentration transport in a typical loop-type fast breeder reactor plant. In the UTOP calculations, the time at which the sodium temperature reaches the reactor trip level is evaluated based on calculated upper plenum flow and temperature distributions. For fission product release from the core assemblies, the delayed neutron precursor concentration in the sodium that reaches the detectors depends on the location of the faulted assembly. Three-dimensional flow patterns, and hence, the residence time in the upper plenum. Delayed neutron precursors that bypassed the recirculation flow to appear in the plenum primarily contribute to the peak concentration.

Prediction and correlations of some delayed neutron precursor yields for certain actinide nuclides

In this paper some predictions about some delayed neutron precursor yields are presented. The predictions are applied for certain actinides with some special interest in the nuclear energy field. The predictions are based on correlations which might be related to the cluster structure of the nucleus.

Transport equation with delayed neutrons

Abstract In nuclear fission reactor, the decay constant of delayed neutron will often determine the time behavior of the neutron population in a subcritical system or supercritical system or in a critical system in which a neutron source or cross section change with time. In the treatment of these problems, it is frequently necessary to include the delayed neutrons. When the effect of delayed neutrons in a reactor system is considered, the time-dependent neutron transport equation will be supplemented with the balance equations for delayed-neutron precursors. The aim of this paper is to present an iterative method for the determination of the solution of transport equation with delayed neutrons and to establish an explicit relationship among these physical parameters of reactor so that one can determine the decay and growth property of the solution of the system. The iterative method consists of two monotone sequences which converge monotonically from above and below, respectively, to a unique solution. Q...

Release Characterization of Delayed Neutron Precursors from Breached FBR Fuel Element

The release behavior of delayed neutron (DN) precursors from the breached fuel was analyzed, based on the diffusional release model. In this analysis, spherical co-ordinate simple approach as well as two-dimensional finite element method were used for the predomiant DN precursor 137I. It was shown that the fuel sodium reaction product (FSRP) layer at the pellet outer surface provided a predominant role for the accelerated release of DN precursors. The macroscopic diffusion coefficient for DN precursors in the FSRP layer was estimated to be 10−9 to 10−10 m2/s, which is greater than that in unreacted fuel by more than about 106. It was demonstrated that the DN signal response correlated to the growth of the FSRP layer, and did not depend on temperature change of interior fuel itself.

Delayed Neutron Data and Group Parameters for 43 Fissioning Systems

The quality and quantity of delayed neutron precursor data have greatly improved over the past decade and a half. Supplementation of the data with model calculations and the use of models to extend the number of precursors to 271 is now practical. These data, along with other improved fission product parameters, permit direct calculations of aggregate behavior for many fissioning nuclides. The results can still be approximated using a few (usually six) temporal groups, including corresponding spectra, as in past practice for reactor physics. An extensive effort to provide a complete set of evaluated data is summarized, with an emphasis on its use to generate the temporal approximations; precursor data and group values are intended for inclusion in ENDF/B-VI.

Release characterization of delayed neutron precursors from breached FBR fuel element.

Release characterization of delayed neutron precursors from breached FBR fuel element.

Theoretical assessment of channel fission gas monitoring vis-à-vis channel DN monitoring for PHWRs

A theoretical assessment of channel fission gas monitoring as against channel delayed neutron (DN) monitoring for pressurized heavy water reactors has been made to enable identification of channels in which failed fuel might reside. The analysis is based on experimentally observed steady-state fractional releases for 133Xe and from it the computed fractional releases for 88Kr, 87Kr, 87Br and 137I. Three types of defective fuel, namely fuel with slow release defects, fast release defects and recoil release defects have been individually considered. Effects of tramp U and fractional release variation on the channel outlet activity of DN precursors have been evaluated. Influences of degassification of the coolant and burst release following a power ramp/trip on the channel ( sig + bkg) bkg ratios have been studied.

Evaluation of Delayed Neutron Data for Thermal Fission of U-235 Based on Integral Experiments at Semi-Homogeneous Experiment

Evaluation of the delayed neutron data for thermal fission of 235U is attempted through an indirect method based on the comparison between measured and calculated integral quantities such as kinetic parameters and reactivity worths of fuel rods and burnable poison rods for the critical assembly Semi-Homogeneous Experiment (SHE). The most probable values for both of the effective delayed neutron fraction βeff and the decay constants λ's of delayed neutron pre-cursors are determined from the condition that the sum of the squared deviations of the ratios of calculated to measured values from unity is minimized for the integral quantities. The most probable value of βeff obtained in the present work is significantly large compared with that obtained with the Keepin's delayed neutron data set, and is closer to the value obtained with the ENDF/8-V data file than that with the ENDF/8-IV. On the other hand, the most probable λ values obtained in the present work are not away from those for thermal fission filed i...

Evaluation of delayed neutron data for thermal fission of U-235 based on integral experiments at semi-homogeneous experiment.

Evaluation of the delayed neutron data for thermal fission of 235U is attempted through an indirect method based on the comparison between measured and calculated integral quantities such as kinetic parameters and reactivity worths of fuel rods and burnable poison rods for the critical assembly Semi-Homogeneous Experiment (SHE). The most probable values for both of the effective delayed neutron fraction βeff and the decay constants λ's of delayed neutron pre-cursors are determined from the condition that the sum of the squared deviations of the ratios of calculated to measured values from unity is minimized for the integral quantities. The most probable value of βeff obtained in the present work is significantly large compared with that obtained with the Keepin's delayed neutron data set, and is closer to the value obtained with the ENDF/8-V data file than that with the ENDF/8-IV. On the other hand, the most probable λ values obtained in the present work are not away from those for thermal fission filed in the Keepin's delayed neutron data set.

Properties of autoregressive model in reactor noise analysis. (I). Convergence of parameters and power spectral density.

Under appropriate conditions, stochastic processes are described by the ARMA model, however, the AR model is popularly used in reactor noise analysis. Hence, the properties of AR model as an approximate representation of the ARMA model should be made clear. Here, convergence of AR-parameters and PSD of AR model were studied through numerical analysis on specific examples such as the neutron noise in subcritical reactors, and it was found that: 1. The convergence of AR-parameters and AR model PSD is governed by the “zero nearest to the unit circle in the complex plane” (μ−1,|μ|<1) of the ARMA model transfer function. 2. The AR-parameters of AR(M) model have biases from those for the infinite model order, and these biases decrease approximately in proportion to |μ|M. 3. The AR model of the neutron noise of subcritical reactors needs a large model order because of an ARMA-zero very close to unity corresponding to the decay constant of the 6-th group of delayed neutron precursors. 4. In applying AR model for ...

Application of evaluated fission-product delayed-neutron precursor data in reactor kinetics calculations

Abstract Evaluated fission-product yield and decay data have been used to describe 105 delayed neutron precursors explicitly in point reactor kinetics calculations. Results calculated for 235U thermal fission show that rod-drop reactivity values obtained from kinetics calculations with 6-group precursor data are considerably higher than those calculated with explicit delayed-neutron precursor data. The calculated kinetics associated with positive reactivity steps are significantly different.