摘要:

AbstractNumerical methods for solving the integrodifferential, integral, and surface-integral forms of the neutron transport equation are reviewed. The solution methods are shown to evolve from only a few basic numerical approximations, such as expansion techniques or the use of quadrature formulas. The emphasis is on the derivation of the approximate equations from the transport equation, and not on the solution of the resulting system of algebraic equations.The presentation covers the approaches used in general-purpose production calculations, including the discrete ordinates finite difference method, the method of characteristics, finite element approximations, the collision-probability method, and nodal methods. Various quasi-analytical techniques for calculating benchmark problems are also treated, such as the singular eigenfunction, spherical harmonics, integral transform, and CNand FNmethods.

ISSN:0029-5639    

DOI:10.13182/NSE80-04-481

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractA complete theory of a direct integration method for solving the steady-state integral transport equation in general geometry is presented together with special techniques for an accurate treatment of monoenergetic radiation source and for mitigation of the ray effect. Emphasis is on several characteristic features, which make the method well adapted to shielding calculations, such as an exact treatment of anisotropic scattering by applying the Klein-Nishina formula for Compton scattering and the differential scattering cross section itself for neutron elastic scattering, analytical integration of the flux term and also direct integration of the source term over the spatial variable in the radiation moving direction, the absence of iterative calculations for obtaining the group angular flux but, instead, applying the point-energy calculation, and optional use of an analytical unscattered flux calculation for mitigating the ray effects.For verifying the validity of the present method, several comparisons of the calculations are presented using the one- and the two-dimensional codes, PALLAS-PL, SP-Br and PALLAS-2DCY-FC, with the experiments adopted as shielding benchmark problems. Fairly good agreement is obtained between PALLAS calculations and experiments on the gamma-ray angular flux spectra at several angles as well as the energy spectra at two and three mean-free-paths in water. For neutron streaming through a cylindrical duct and also an annular duct, PALLAS calculations are in fairly good agreement with experiments in terms of the reaction rate except for thermal neutrons, where an obvious underestimation is obtained. For neutron deep penetration in an iron shield, selected for examining the weakest point of the method, a PALLAS calculation is found to be adequate for shielding design calculations, though some discrepancy is seen between calculation and experiment on neutron energy spectra at 20- and 30-in. depths.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18968

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractA numerical method is presented for calculating neutron transport problems in three-dimensional (x,y,z) geometry on the basis of a method of direct integration of the integral transport equation. Several new techniques are introduced to the method to make it well adapted to practical neutron transport calculations in three-dimensional geometry. A technique for evaluating the scattering source based on an estimated spectral shape in each material region allows use of coarse energy mesh intervals without reducing calculational accuracy as compared with the calculation with fine meshes. A quadratic function approximation for the source spatial distribution in each spatial mesh interval is found to improve the mathematical error in direct integration of the source term over the spatial variable as compared with the linear- or exponential-function approximation used in the original method. In addition, Lagrange’s interpolation formula is applied instead of the linear interpolation used in the original method for more accurate estimation of both flux and source.Comparisons are made of the calculations with experiments for three neutron transport problems, the pool critical assembly experiment, the Winfrith iron benchmark experiment, and the annular duct neutron streaming experiment, and also with the three-dimensional Sncalculation to verify the validity of the present method for neutron transport calculations in (x,y,z) geometry.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18969

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractFor transport problems with fine energy group structure, the group-to-group transfer cross sections are usually quite anisotropic in the scattering angle. It is shown for neutron inelastic scattering that explicit use of the characteristic shape of these transfer cross sections permits more efficient and accurate numerical evaluation of their Legendre expansion coefficients than is afforded by existing techniques. In addition, transfer cross sections can often be well approximated by piecewise, low-order polynomials with which very accurate and simple expressions can be derived for the Legendre coefficients. This analytical approach both minimizes the access of nuclear data files and accurately determines even the higher order coefficients.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18970

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractThe inner integral over final particle energy or collision cosine of the multigroup transfer matrix is evaluated analytically for the general nonrelativistic two-body interaction. Under the condition that the center-of-mass angular distribution is piecewise linear, the solution is exact.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18971

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractIntegral experiments that measure the streaming of∼14-MeV neutrons through a 0.30-m-diam iron duct (length-to-diameter ratio∼3) imbedded in a concrete shield have been carried out at the Oak Ridge National Laboratory. Calculated and measured neutron and gamma-ray energy spectra are compared at 16 detector locations on and off the cylindrical axis of the duct. The measured spectra were obtained using an NE-213 liquid scintillator detector with pulse-shape discrimination to simultaneously resolve neutron and gamma-ray events. The calculated spectra were obtained using a computer code network that incorporates two radiation transport methods: discrete ordinates (with P3multigroup cross sections) and Monte Carlo (with continuous point cross sections). The two radiation transport methodologies are required to properly account for neutrons that single scatter from the duct to the detector. The calculated and measured outgoing neutron energy spectra above 850 keV agree within 5 to 50% depending on detector location and neutron energy. The calculated and measured gamma-ray spectra above 750 ke V are also in favorable agreement,∼5 to 50%, depending on detector location and gamma-ray energy.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18972

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractThe Oak Ridge National Laboratory large liquid-scintillator detector was used in a precise determination of v̄p, the number of neutrons emitted promptly, from spontaneous fission of252Cf. Measurements of the detector efficiency over a broad energy region were made by means of a proton-recoil technique employing the Oak Ridge Electron Linear Accelerator“white”neutron source. Monte Carlo calculation of the detector efficiency for a spectrum representative of252Cf fission neutrons was calibrated with these elaborate measurements. The unusually flat response of the neutron detector resulted in elimination of several known sources of error. Experimental measurement was coupled with calculational methods to correct for other known errors. These measurements lead to an unusually small estimated uncertainty of 0.2% in the value obtained, v̄p= 3.773±0.007.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18973

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractThe capture cross sections of93Nb,103Rh, and181Ta were measured in the 10- to 70-keV neutron energy range, using197Au as a standard. Most of the data points were obtained with a total uncertainty of∼4%. This was possible because the calculation of capture gamma-ray spectra allowed reducing the most severe systematic uncertainties involved. Hauser-Feshbach calculations were performed that yielded not only the neutron cross sections of the isotopes considered up to 4-MeV neutron energy but also partial capture cross sections and capture gamma-ray spectra. For these calculations a consistent set of input parameters was determined from available experimental information or from model-guided systematics. The influence of these parameters on the results is discussed.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18974

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractA coarse mesh nodal coupling method, a well-known technique often used in steady-state neutronics analysis of light water reactors, is extended to a problem of transient phenomena of boiling water reactors (BWRs). Spatial collapse is attempted to develop a multiregion neutronics model and the associated axially one-dimensional and one-point models.These models are numerically solved through the use of two approximations, quasi-static and prompt jump. The results as applied to a reference BWR core for transient analyses, initiated by artificial thermal-hydraulic disturbances, are presented to show the practicality of the approach.The nature of the optimal weighting function necessary for the spatial collapse and for the quasi-static approximation is also discussed.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18975

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor

摘要:

AbstractSodium evaporation rates from Karlsruhe Nuclear Research Center-NALA experiments (experiments on aerosol release from a contaminated sodium pool into an argon or a nitrogen atmosphere) are presented. Pool temperatures were varied between 700 and 1000 K at different geometrical and convective conditions. Technical scale experiments with a 531-cm2pool surface area were performed at natural convection in a 2.2-m3heated vessel, as well as additional small scale experiments at forced convection and 38.5-cm2pool surface area. The data are compared to the sodium vapor pressure. For the data at natural convection, a best fit formula is given.

ISSN:0029-5639    

DOI:10.13182/NSE82-A18976

出版商:Taylor&Francis    

年代:1982

数据来源: Taylor