The P1approximation in the transport of beta rays
International Nuclear Information System (INIS)
Legarda, F.; Idoeta, R.; Herranz, M.
1994-01-01
A validation test for the p1 approximation to the linear transport of electrons in planar geometry has been performed. The p1 approximation is shown to be a good option for the description of the transport of beta rays with endpoint energies between 400kev and 3.5Mev through aluminium foils . This approximation together with the use of only elastic interactions of electrons with atoms has found good agreement with experimental results . A calculation has been made of the fraction of transmitted electrons through foils, solving the transport equation for planar geometry in the p1 approximation and assuming that only elastic scattering processes take place. The boundary condition at the entrance of the foil was a collimated beta source, while at the end of the foil has been adopted a vaccum boundary condition.Sources considered are those for which experimental and calculated spectrum shapes are known to agree. The calculated fractional transmission through different absorber thicknesses is found to have an exponential shape . Besides this fact the attenuation coefficients found ,when compared with those empirically obtained, agree to within 5%. 1 fig.; 4 refs. (author)
The P1-approximation for the Distribution of Neutrons from a Pulsed Source in Hydrogen
International Nuclear Information System (INIS)
Claesson, A.
1963-12-01
The asymptotic distribution of neutrons from a pulsed, high energy source in an infinite moderator has been obtained earlier in a 'diffusion' approximation. In that paper the cross section was assumed to be constant over the whole energy region and the time derivative of the first moment was disregarded. Here, first, an analytic expression is obtained for the density in a P 1 -approximation. However, the result is very complicated, and it is shown that an asymptotic solution can be found in a simpler way. By taking into account the low hydrogen scattering cross section at the source energy it follows that the space dependence of the distribution is less than that obtained earlier. The importance of keeping the time derivative of the first moment is further shown in a perturbation approximation
Neutron wave reflexions in interface media with transport equation P1 approximation
International Nuclear Information System (INIS)
Oliveira Vellozo, S. de.
1977-01-01
The propagation of neutron waves in non multiplying media is investigated employing the Telegrapher's equation obtained from the P 1 approximation of the time, space and energy dependent Boltzmann equation. Solution of the problem of propagation of sinusoidally modulated source incident on one face of the medium is obtained by analysing the Fourier component of a pulsed source introduced, for the corresponding frequency. The amplitude and the phase of the flux are computed as a function of frequency in media consisting of one, two and three regions in order to study the effects of reflection at the interfaces. The results are compared with those from the Diffusion approximation obtained by neglecting the term involving the second order time derivative. (author)
International Nuclear Information System (INIS)
Musazay, M.S.
1981-01-01
A solution to the space and energy dependent neutron transport equation in the framework of the consistent P-1 approximation is sought. The transport equation for thermal neutrons in a moderator of 1/v absorption and constant scattering cross section is changed into a set of coupled partial differential equations. The space dependent part is removed by assuming a cosine shaped flux due to a cosine shaped source at a very high energy. The resulting set of strongly coupled ordinary differential equations is decoupled by assuming expansion of collision density in the powers of a leakage parameter whose coefficients are energy and absorption dependent. These energy dependent coefficients are solutions of a set of weakly coupled differential equations. Series solutions to these differential equations in powers of epsilon and 1/epsilon, where epsilon = E/kT, E being the neutron energy and kT the moderator temperature in units of energy, are found. The properties of these solutions are studied extensively. Absorption appears as a parameter in the coefficients of the series. The difficulties arising in choosing the correct form of the asymptotic solutions are resolved by comparing slowing and thermalization. The limitations on the size of the slab and on the range of absorption are included in the analysis
International Nuclear Information System (INIS)
Ligou, J.; Thomi, P.A.
1973-01-01
1 - Nature of physical problem solved: Integral transport equation, anisotropy of diffusion in P1 approximation. SHADOK3 - cylindrical geometry; direct solution of the linear system. SHADOK4 - cylindrical geometry; Thermalization iteration; solution of the linear system with inverse matrix calculation. SHADOK5 - like SHADOK3 for spherical geometry. SHADOK6 - like SHADOK4 for spherical geometry. 2 - Method of solution: Analysis in terms of annuli for each of which polynomial approximation is applied. Dynamic allocation (for formulas see report TM(10)). 3 - Restrictions on the complexity of the problem: Relative accuracy of the Bickley functions about 1.0E-13
Variational P1 approximations of general-geometry multigroup transport problems
International Nuclear Information System (INIS)
Rulko, R.P.; Tomasevic, D.; Larsen, E.W.
1995-01-01
A variational approximation is developed for general-geometry multigroup transport problems with arbitrary anisotropic scattering. The variational principle is based on a functional that approximates a reaction rate in a subdomain of the system. In principle, approximations that result from this functional ''optimally'' determine such reaction rates. The functional contains an arbitrary parameter α and requires the approximate solutions of a forward and an adjoint transport problem. If the basis functions for the forward and adjoint solutions are chosen to be linear functions of the angular variable Ω, the functional yields the familiar multigroup P 1 equations for all values of α. However, the boundary conditions that result from the functional depend on α. In particular, for problems with vacuum boundaries, one obtains the conventional mixed boundary condition, but with an extrapolation distance that depends continuously on α. The choice α = 0 yields a generalization of boundary conditions derived earlier by Federighi and Pomraning for a more limited class of problems. The choice α = 1 yields a generalization of boundary conditions derived previously by Davis for monoenergetic problems. Other boundary conditions are obtained by choosing different values of α. The authors discuss this indeterminancy of α in conjunction with numerical experiments
Theory and control calculations. Application to BWR and PWR
International Nuclear Information System (INIS)
Velarde, G.; Guerra, J.
1972-01-01
A theoretical method to extend the applicability of P 1 approximation to strong absorbers is given. Tables of effective diffusion parameters for slab and cylindrical geometry as well as a summary of expressions for obtaining the extrapolation length in cases of interest, are included. (Author) 21 refs
TRIMARAN: a three dimensional multigroup P1 Monte Carlo code for criticality studies
International Nuclear Information System (INIS)
Ermumcu, G.; Gonnord, J.; Nimal, J.C.
1980-01-01
TRIMARAN is developed for safety analysis of nuclear components containing fissionable materials: shipping casks, storage and cooling pools, manufacture and reprocessing plants. It solves the transport equation by Monte Carlo method, in general three dimensional geometry with multigroup P1 approximation. A special representation of cross sections and numbers has been developed in order to reduce considerably the computing cost and allow this three dimensional code to compete with standard numerical program used in parametric studies
TRIMARAN: a three dimensional multigroup P1 Monte Carlo code for criticallity studies
International Nuclear Information System (INIS)
Ermuncu, G.; Gonnord, J.; Nimal, J.C.
1980-04-01
TRIMARAN is developed for safety analysis of nuclar components containing fissionnable materials: shipping casks, storage and cooling pools, manufacture and reprocessing plants. It solves the transport equation by Monte Carlo method in general three dimensional geometry with multigroup P1 approximation. A special representation of cross sections and numbers has been developed in order to reduce considerably the computing cost and allow this three dimensional code to compete with standard numerical program used in parametric studies
International Nuclear Information System (INIS)
Boukadida, T.
1988-01-01
The compatibility between accuracy and stability of the quasilinear equations is studied. Three stuations are analyzed: the discontinuous P-1 approximation of the first order quasilinear equation, the two dimensional version of the Lax-Friedrichs scheme and the coupling of modes in a plasma. For the one dimensional case, the proposed scheme matches the available data. In the two dimensional case, tests to show the explosion condition are performed. This investigation can be applied in laser-matter interactions, nonlinear optics and in many fields of physics [fr
International Nuclear Information System (INIS)
Androsenko, A.A.; Androsenko, P.A.; Kagalenko, I.Eh.; Mironovich, Yu.N.
1992-01-01
Consideration is given of a technique and algorithms of constructing neutron trajectories in the Monte-Carlo method taking into account the data on adjoint transport equation solution. When simulating the transport part of transfer kernel the use is made of piecewise-linear approximation of free path length density along the particle motion direction. The approach has been implemented in programs within the framework of the BRAND code system. The importance is calculated in the multigroup P 1 -approximation within the framework of the DD-30 code system. The efficiency of the developed computation technique is demonstrated by means of solution of two model problems. 4 refs.; 2 tabs
Program system for computation of the terrestrial gamma-radiation field
International Nuclear Information System (INIS)
Kirkegaard, P.; Loevborg, L.
1979-02-01
A system of computer programs intended for solution of the plane one-dimensional photon transport equation in the case of two adjacent media is described, and user's guides for the programs are given. One medium represents a natural ground with uniformly distributed potassium, uranium, and thorium gamma-ray emitters. The other medium is usually air with no radioactive contaminants. The solution method is the double-P 1 approximation with logarithmic energy spacing. The complete data-processing system GB contains the transport-theory code GAMP1, the code GFX for computation of scalar flux and dose rate, and a number of auxiliary programs and data files. (author)
Specific features of time-dependent Psub(N) approximations in spherical geometry
International Nuclear Information System (INIS)
Peltzer, P.; Pucker, N.
1979-01-01
Approximations to the time-dependent linear transport equation can result in more serious distortions in the description of the actual physical situation than in the stationary problem. This is demonstrated in detail for the case of a neutron pulse in spherical geometry, treated within a P 1 approximation. One has to pay special attention to the singularity at r = 0 and to the effect of the boundary conditions. Effects similar to those shown here are also to be expected in connection with Psub(N) approximations of higher order. (Auth.)
Multigroup Approximation of Radiation Transfer in SF6 Arc Plasmas
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Milada Bartlova
2013-01-01
Full Text Available The first order of the method of spherical harmonics (P1-approximation has been used to evaluate the radiation properties of arc plasmas of various mixtures of SF6 and PTFE ((C2F4n, polytetrafluoroethylene in the temperature range (1000 ÷ 35 000 K and pressures from 0.5 to 5 MPa. Calculations have been performed for isothermal cylindrical plasma of various radii (0.01 ÷ 10 cm. The frequency dependence of the absorption coefficients has been handled using the Planck and Rosseland averaging methods for several frequency intervals. Results obtained using various means calculated for different choices of frequency intervals are discussed.
International Nuclear Information System (INIS)
Wang, Fuqiang; Tan, Jianyu; Shuai, Yong; Gong, Liang; Tan, Heping
2014-01-01
Highlights: • H 2 production by hybrid solar energy and methane steam reforming is analyzed. • MCRT and FVM coupling method is used for chemical reaction in solar porous reactor. • LTNE model is used to study the solid phase and fluid phase thermal performance. • Modified P1 approximation programmed by UDFs is used for irradiative heat transfer. - Abstract: The calorific value of syngas can be greatly upgraded during the methane steam reforming process by using concentrated solar energy as heat source. In this study, the Monte Carlo Ray Tracing (MCRT) and Finite Volume Method (FVM) coupling method is developed to investigate the hydrogen production performance via methane steam reforming in porous media solar thermochemical reactor which includes the mass, momentum, energy and irradiative transfer equations as well as chemical reaction kinetics. The local thermal non-equilibrium (LTNE) model is used to provide more temperature information. The modified P1 approximation is adopted for solving the irradiative heat transfer equation. The MCRT method is used to calculate the sunlight concentration and transmission problems. The fluid phase energy equation and transport equations are solved by Fluent software. The solid phase energy equation, irradiative transfer equation and chemical reaction kinetics are programmed by user defined functions (UDFs). The numerical results indicate that concentrated solar irradiation on the fluid entrance surface of solar chemical reactor is highly uneven, and temperature distribution has significant influence on hydrogen production
International Nuclear Information System (INIS)
Wang, Fuqiang; Tan, Jianyu; Ma, Lanxin; Leng, Yu
2015-01-01
Highlights: • Effects of key factors on chemical reaction for solar methane reforming are studied. • MCRT and FVM method coupled with UDFs is used to establish numerical model. • Heat and mass transfer model coupled with thermochemical reaction is established. • LTNE model coupled with P1 approximation is used for porous matrix solar reactor. • A formula between H 2 production and conductivity of porous matrix is put forward. - Abstract: With the aid of solar energy, methane reforming process can save up to 20% of the total methane consumption. Monte Carlo Ray Tracing (MCRT) method and Finite Volume Method (FVM) combined method are developed to establish the heat and mass transfer model coupled with thermochemical reaction kinetics for porous medium solar thermochemical reactor. In order to provide more temperature information, local thermal non-equilibrium (LTNE) model coupled with P1 approximation is established to investigate the thermal performance of porous medium solar thermochemical reaction. Effects of radiative heat loss and thermal conductivity of porous matrix on temperature distribution and thermochemical reaction for solar driven steam methane reforming process are numerically studied. Besides, the relationship between hydrogen production and thermal conductivity of porous matrix are analyzed. The results illustrate that hydrogen production shows a 3 order polynomial relation with thermal conductivity of porous matrix
Analysis of cavity effect on space- and time-dependent fast and thermal neutron energy spectra
International Nuclear Information System (INIS)
Kudo, Katsuhisa; Narita, Masakuni; Ozawa, Yasutomo.
1975-01-01
The effects of the presence of a central cavity on the space- and time-dependent neutron energy spectra in both thermal and fast neutron systems are analyzed theoretically with use made of the multi-group one-dimensional time-dependent Ssub(n) method. The thermal neutron field is also analyzed for the case of a fundamental time eigenvalue problem with the time-dependent P 1 approximation. The cavity radius is variable, and the system radius for graphite is 120 cm and for the other materials 7 cm. From the analysis of the time-dependent Ssub(n) calculations in the non-multiplying systems of polythene, light water and graphite, cavity heating is the dominant effect for the slowing-down spectrum in the initial period following fast neutron burst, and when the slowing-down spectrum comes into the thermal energy region, cavity heating shifts to cavity cooling. In the multiplying system of 235 U, cavity cooling also takes place as the spectrum approaches equilibrium after the fast neutron burst is injected. The mechanism of cavity cooling is explained analytically for the case of thermal neutron field to illustrate its physical aspects, using the time-dependent P 1 approximation. An example is given for the case of light water. (auth.)
A coordinate transform method for one-speed neutron transport in composite slabs
International Nuclear Information System (INIS)
Haidar, N.H.S.
1988-01-01
The optical path transformation is applied to reduce the one-speed neutron transport equation for a class of composite subcritical slabs to single-region problems. The class idealises, within the uncertainty of the one-speed model, a variety of practical situations such as U-D 2 O-C-Zr-Pb or Pu-U-Na-Fe symmetric reactor assemblies; which may possibly contain a symmetrically anisotropic neutron source. A closed form double series solution, which turns out to be quite convenient for design and optimisation purposes, has been obtained, in terms of discontinuous functions for the multi-regional angular flux by application of a double finite Legendre transform. Disadvantage factor evaluations for a U-C lattice cell resulting from a low-order P 0 P 1 approximation of this method are found to be in full agreement with hybrid diffusion-transport estimates. (author)
Hartung, Lin C.; Hassan, H. A.
1992-01-01
A moment method for computing 3-D radiative transport is applied to axisymmetric flows in thermochemical nonequilibrium. Such flows are representative of proposed aerobrake missions. The method uses the P-1 approximation to reduce the governing system of integro-di erential equations to a coupled set of partial di erential equations. A numerical solution method for these equations given actual variations of the radiation properties in thermochemical nonequilibrium blunt body flows is developed. Initial results from the method are shown and compared to tangent slab calculations. The agreement between the transport methods is found to be about 10 percent in the stagnation region, with the difference increasing along the flank of the vehicle.
International Nuclear Information System (INIS)
Sahin, S.; Selvi, S.
1980-01-01
The suitability of borated reflector drums has been investigated and shown as a control mechanism for space craft thermionic reactors with constant emitter heating using U-233 as fuel and beryllium to be moderator, mainly due to their extremce compactness and their very soft neutron sepctrum. The achievable change in ksub(eff) allows long-term control operation with success. The use of reflector drums keeps the cone diameter and the mass of the radiation shield on minimum. The distortion of the emitter heating field remains under acceptable tolerances, mainly due to the enhanced neutron production at the outer core region and the remaining reflector part between the boron layer and the core. All neutron physics calculations have been carried out using the multigroup Ssub(N) methods. Three data groups for r-theta-calculations in S 4 -P 1 approximation (16 space angles) have been evaluated from a 123-energy-groups data library using transport theoretical methods. (orig.) [de
The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer
International Nuclear Information System (INIS)
Modest, M.F.
1991-01-01
In this paper the weighted-sum-of-gray-gases approach for radiative transfer in non-gray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (non-scattering media within a black-walled enclosure) any non-gray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-1 approximation of the equivalent gray media solution. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95%) which are achieved
A Laplace transform method for energy multigroup hybrid discrete ordinates
International Nuclear Information System (INIS)
Segatto, C.F.; Vilhena, M.T.; Barros, R.C.
2010-01-01
In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S 2 method (P 1 approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS N ) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.
International Nuclear Information System (INIS)
Gerardin, J.
2012-01-01
We developed a method of resolution of radiative transfer inside a medium of vapor-droplets surrounded by hot walls, in order to couple it with a simulation of the flow at the CFD scale. The scope is the study of the cooling of the core of nuclear reactor following a Loss Of Coolant Accident (LOCA). The problem of radiative transfer can be cut into two sub problems, one concerning the evaluation of the radiative properties of the medium and a second concerning the solution of the radiative transfer equation. The radiative properties of the droplets have been computed with the use of the Mie Theory and those of the vapor have been computed with a Ck model. The medium made of vapor and droplets is an absorbing, anisotropically scattering, emissive, non grey, non homogeneous medium. Hence, owing to the possible variations of the flow properties (diameter and volumetric fraction of the droplets, temperature and pressure of the vapor), the medium can be optically thin or thick. Consequently, a method is required which solves the radiative transfer accurately, with a moderate calculation time for all of these prerequisites. The IDA has been chosen, derived from the well-known P1-approximation. Its accuracy has been checked on academical cases found in the literature and by comparison with experimental data. Simulations of LOCA flows have been conducted taking account of the radiative transfer, evaluating the radiative fluxes and showing that radiative transfer influence cannot be neglected. (author)
The Coupling of Radiation and Hydrodynamics
International Nuclear Information System (INIS)
Lowrie, R.B.; Morel, J.E.; Hittinger, J.A.
1999-01-01
The coupling of radiation transport and hydrodynamics is discussed for the Eulerian frame. The discussion is aimed at developing a suitable set of equations for nonrelativistic radiation hydrodynamics (RHD) that can be numerically integrated using high-resolution methods for conservation laws. We outline how numerical methods based on a wave decomposition may be developed, along with the importance of conservation, particularly in the equilibrium regime. The properties of the RHD equations are examined through asymptotic and dispersion analyses. The conditions required to obtain the classical equilibrium limit are rigorously studied. The results show that a simple coupling term developed recently by Morel, which retains a minimum of relativistic corrections, may be sufficient for nonrelativistic flows. We also give two constraints on the relativistic corrections that result in retaining terms on the order of the truncation. In addition, the dispersion results for the P 1 approximation are studied in detail and are compared with both the exact-transport results and a full relativistic treatment. We also examine some nonintuitive behavior in the dispersion results. copyright copyright 1999. The American Astronomical Society
Numerical modeling of soot formation in a turbulent C2H4/air diffusion flame
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Manedhar Reddy Busupally
2016-06-01
Full Text Available Soot formation in a lifted C2H4-Air turbulent diffusion flame is studied using two different paths for soot nucleation and oxidation; by a 2D axisymmetric RANS simulation using ANSYS FLUENT 15.0. The turbulence-chemistry interactions are modeled using two different approaches: steady laminar flamelet approach and flamelet-generated manifold. Chemical mechanism is represented by POLIMI to study the effect of species concentration on soot formation. P1 approximation is employed to approximate the radiative transfer equation into truncated series expansion in spherical harmonics while the weighted sum of gray gases is invoked to model the absorption coefficient while the soot model accounts for nucleation, coagulation, surface growth, and oxidation. The first route for nucleation considers acetylene concentration as a linear function of soot nucleation rate, whereas the second route considers two and three ring aromatic species as function of nucleation rate. Equilibrium-based and instantaneous approach has been used to estimate the OH concentration for soot oxidation. Lee and Fenimore-Jones soot oxidation models are studied to shed light on the effect of OH on soot oxidation. Moreover, the soot-radiation interactions are also included in terms of absorption coefficient of soot. Furthermore, the soot-turbulence interactions have been invoked using a temperature/mixture fraction-based single variable PDF. Both the turbulence-chemistry interaction models are able to accurately predict the flame liftoff height, and for accurate prediction of flame length, radiative heat loss should be accounted in an accurate way. The soot-turbulence interactions are found sensitive to the PDF used in present study.
Martin, Heath T.
2015-01-01
Due to the severity of the internal solid rocket motor (SRM) environment, very few direct measurements of that environment exist; therefore, the appearance of such data provides a unique opportunity to assess current thermal/fluid modeling capabilities. As part of a previous study of SRM internal insulation performance, the internal thermal environment of a laboratory-scale SRM featuring aluminized propellant was characterized with two types of custom heat-flux calorimeters: one that measured the total heat flux to a graphite slab within the SRM chamber and another that measured the thermal radiation flux. Therefore, in the current study, a thermal/fluid model of this lab-scale SRM was constructed using ANSYS Fluent to predict not only the flow field structure within the SRM and the convective heat transfer to the interior walls, but also the resulting dispersion of alumina droplets and the radiative heat transfer to the interior walls. The dispersion of alumina droplets within the SRM chamber was determined by employing the Lagrangian discrete phase model that was fully coupled to the Eulerian gas-phase flow. The P1-approximation was engaged to model the radiative heat transfer through the SRM chamber where the radiative contributions of the gas phase were ignored and the aggregate radiative properties of the alumina dispersion were computed from the radiative properties of its individual constituent droplets, which were sourced from literature. The convective and radiative heat fluxes computed from the thermal/fluid model were then compared with those measured in the lab-scale SRM test firings and the modeling approach evaluated.
Validation of a Solid Rocket Motor Internal Environment Model
Martin, Heath T.
2017-01-01
In a prior effort, a thermal/fluid model of the interior of Penn State University's laboratory-scale Insulation Test Motor (ITM) was constructed to predict both the convective and radiative heat transfer to the interior walls of the ITM with a minimum of empiricism. These predictions were then compared to values of total and radiative heat flux measured in a previous series of ITM test firings to assess the capabilities and shortcomings of the chosen modeling approach. Though the calculated fluxes reasonably agreed with those measured during testing, this exercise revealed means of improving the fidelity of the model to, in the case of the thermal radiation, enable direct comparison of the measured and calculated fluxes and, for the total heat flux, compute a value indicative of the average measured condition. By replacing the P1-Approximation with the discrete ordinates (DO) model for the solution of the gray radiative transfer equation, the radiation intensity field in the optically thin region near the radiometer is accurately estimated, allowing the thermal radiation flux to be calculated on the heat-flux sensor itself, which was then compared directly to the measured values. Though the fully coupling the wall thermal response with the flow model was not attempted due to the excessive computational time required, a separate wall thermal response model was used to better estimate the average temperature of the graphite surfaces upstream of the heat flux gauges and improve the accuracy of both the total and radiative heat flux computations. The success of this modeling approach increases confidence in the ability of state-of-the-art thermal and fluid modeling to accurately predict SRM internal environments, offers corrections to older methods, and supplies a tool for further studies of the dynamics of SRM interiors.
Improved age-diffusion model for low-energy electron transport in solids. I. Theory
International Nuclear Information System (INIS)
Devooght, J.; Dubus, A.; Dehaes, J.C.
1987-01-01
We have developed in this paper a semianalytical electron transport model designed for parametric studies of secondary-electron emission induced by low-energy electrons (keV range) and by fast light ions (100 keV range). The primary-particle transport is assumed to be known and to give rise to an internal electron source. The importance of the nearly isotropic elastic scattering in the secondary-electron energy range (50 eV) and the slowing-down process strongly reduce the influence of the anisotropy of the internal electron source, and the internal electron flux is nearly isotropic as is evidenced by the experimental results. The differential energy behavior of the inelastic scattering kernel is very complicated and the real kernel is replaced by a synthetic scattering kernel of which parameters are obtained by energy and angle moments conservation. Through a P 1 approximation and the use of the synthetic scattering kernel, the Boltzmann equation is approximated by a diffusion--slowing-down equation for the isotropic part of the internal electron flux. The energy-dependent partial reflection boundary condition reduces to a Neumann-Dirichlet boundary condition. An analytical expression for the Green's function of the diffusion--slowing-down equation with the surface boundary condition is obtained by means of approximations close to the age-diffusion theory and the model allows for transient conditions. Independently from the ''improved age-diffusion'' model, a correction formula is developed in order to take into account the backscattering of primary electrons for an incident-electron problem
Neutron slowing-down time in finite water systems
International Nuclear Information System (INIS)
Hirschberg, S.
1981-11-01
The influence of the size of a moderator system on the neutron slowing-down time has been investigated. The experimental part of the study was performed on six cubes of water with side lengths from 8 to 30 cm. Neutrons generated in pulses of about 1 ns width were slowed down from 14 MeV to 1.457 eV. The detection method used was based on registration of gamma radiation from the main capture resonance of indium. The most probable slowing-down times were found to be 778 +- 23 ns and 898 +- 25 ns for the smallest and for the largest cubes, respectively. The corresponding mean slowing-down times were 1205 +- 42 ns and 1311 +- 42 ns. In a separate measurement series the space dependence of the slowing-down time close to the source was studied. These experiments were supplemented by a theoretical calculation which gave an indication of the space dependence of the slowingdown time in finite systems. The experimental results were compared to the slowing-down times obtained from various theoretical approaches and from Monte Carlo calculations. All the methods show a decrease of the slowing-down time with decreasing size of the moderator. This effect was least pronounced in the experimental results, which can be explained by the fact the measurements are spatially dependent. The agreement between the Monte Carlo results and those obtained using the diffusion approximation or the age-diffusion theory is surprisingly good, especially for large systems. The P1 approximation, on the other hand, leads to an overestimation of the effect of the finite size on the slowing-down time. (author)
CFD simulation of the combustion process of the low-emission vortex boiler
Chernov, A. A.; Maryandyshev, P. A.; Pankratov, E. V.; Lubov, V. K.
2017-11-01
Domestic heat and power engineering needs means and methods for optimizing the existing boiler plants in order to increase their technical, economic and environmental work. The development of modern computer technology, methods of numerical modeling and specialized software greatly facilitates the solution of many emerging problems. CFD simulation allows to obtaine precise results of thermochemical and aerodynamic processes taking place in the furnace of boilers in order to optimize their operation modes and develop directions for their modernization. The paper presents the results of simulation of the combustion process of a low-emission vortex coal boiler of the model E-220/100 using the software package Ansys Fluent. A hexahedral grid with a number of 2 million cells was constructed for the chosen boiler model. A stationary problem with a two-phase flow was solved. The gaseous components are air, combustion products and volatile substances. The solid phase is coal particles at different burnup stages. The Euler-Lagrange approach was taken as a basis. Calculation of the coal particles trajectories was carried out using the Discrete Phase Model which distribution of the size particle of coal dust was accounted for using the Rosin-Rammler equation. Partially Premixed combustion model was used as the combustion model which take into account elemental composition of the fuel and heat analysis. To take turbulence into account, a two-parameter k-ε model with a standard wall function was chosen. Heat transfer by radiation was calculated using the P1-approximation of the method of spherical harmonics. The system of spatial equations was numerically solved by the control volume method using the SIMPLE algorithm of Patankar and Spaulding. Comparison of data obtained during the industrial-operational tests of low-emission vortex boilers with the results of mathematical modeling showed acceptable convergence of the tasks of this level, which confirms the adequacy of the
Directory of Open Access Journals (Sweden)
Lauren L. Jantzie
2018-04-01
Full Text Available Cerebral palsy (CP is the leading cause of motor impairment for children worldwide and results from perinatal brain injury (PBI. To test novel therapeutics to mitigate deficits from PBI, we developed a rat model of extreme preterm birth (<28 weeks of gestation that mimics dual intrauterine injury from placental underperfusion and chorioamnionitis. We hypothesized that a sustained postnatal treatment regimen that combines the endogenous neuroreparative agents erythropoietin (EPO and melatonin (MLT would mitigate molecular, sensorimotor, and cognitive abnormalities in adults rats following prenatal injury. On embryonic day 18 (E18, a laparotomy was performed in pregnant Sprague–Dawley rats. Uterine artery occlusion was performed for 60 min to induce placental insufficiency via transient systemic hypoxia-ischemia, followed by intra-amniotic injections of lipopolysaccharide, and laparotomy closure. On postnatal day 1 (P1, approximately equivalent to 30 weeks of gestation, injured rats were randomized to an extended EPO + MLT treatment regimen, or vehicle (sterile saline from P1 to P10. Behavioral assays were performed along an extended developmental time course (n = 6–29. Open field testing shows injured rats exhibit hypermobility and disinhibition and that combined neonatal EPO + MLT treatment repairs disinhibition in injured rats, while EPO alone does not. Furthermore, EPO + MLT normalizes hindlimb deficits, including reduced paw area and paw pressure at peak stance, and elevated percent shared stance after prenatal injury. Injured rats had fewer social interactions than shams, and EPO + MLT normalized social drive. Touchscreen operant chamber testing of visual discrimination and reversal shows that EPO + MLT at least partially normalizes theses complex cognitive tasks. Together, these data indicate EPO + MLT can potentially repair multiple sensorimotor, cognitive, and behavioral realms following PBI, using
GAPER-1D, 1-D Multigroup 1. Order Perturbation Transport Theory for Reactivity Coefficient
International Nuclear Information System (INIS)
Koch, P.K.
1976-01-01
1 - Description of problem or function: Reactivity coefficients are computed using first-order transport perturbation theory for one- dimensional multi-region reactor assemblies. The number of spatial mesh-points and energy groups is arbitrary. An elementary synthesis scheme is employed for treatment of two- and three-dimensional problems. The contributions to the change in inverse multiplication factor, delta(1/k), from perturbations in the individual capture, net fission, total scattering, (n,2n), inelastic scattering, and leakage cross sections are computed. A multi-dimensional prompt neutron lifetime calculation is also available. 2 - Method of solution: Broad group cross sections for the core and perturbing or sample materials are required as input. Scalar neutron fluxes and currents, as computed by SN transport calculations, are then utilized to solve the first-order transport perturbation theory equations. A synthesis scheme is used, along with independent SN calculations in two or three dimensions, to treat a multi- dimensional assembly. Spherical harmonics expansions of the angular fluxes and scattering source terms are used with leakage and anisotropic scattering treated in a P1 approximation. The angular integrations in the perturbation theory equations are performed analytically. Various reactivity coefficients and material worths are then easily computed at specified positions in the assembly. 3 - Restrictions on the complexity of the problem: The formulation of the synthesis scheme used for two- and three-dimensional problems assumes that the fluxes and currents were computed by the DTF4 code (NESC Abstract 209). Therefore, fluxes and currents from two- or three-dimensional transport or diffusion theory codes cannot be used
BOLD/VENTURE-4, Reactor Analysis System with Sensitivity and Burnup
International Nuclear Information System (INIS)
1998-01-01
cross section variation or correlation on nuclide concentrations is provided, but a temperature dependence is coded. Steady state condition with continuous fueling is established by a global iterative scheme that applies the criticality search scheme in the neutronics and models fuel movement directly in the exposure code. Time-dependent sensitivity data applies the forward march, reverse importance approach. The codes do not process data from the user input data stream allowing flexible task assignment along selected calculational paths. Multigroup cross section data are produced locally using the PSR-0063/AMPX II or CCC-0450/SCALE-2 code systems to produce resonance shielding (NITAWL) and cell weighted (XSDRN) microscopic cross sections. Locally, each code is compiled and loaded, and only one version is maintained in a quality assurance state in load module form. An on-line catalog procedure, installed with system support, provides job control instructions with nominal default of space allocation to files. Executing the catalog procedure makes the driver memory resident. The first user input data line must be the control module name used for the run. VENTURE-PC: The VENTURE module applies the finite-difference diffusion or a simple P1 approximation. VENTURE uses an outer-inner iteration scheme with several different data handling methods. Over-relaxation is applied to the inner and outer iterations, and succeeding flux iterates may be accelerated with the Chebychev process. - The BURNER code (module EXPOSURE) uses a difference formulation based on average generation rates; or a matrix exponential formulation to approximate the solution of the coupled burnup differential equations; or an explicit solution for simply coupled nuclide chains. Space dependence is included by working with zone averaged fluxes
VENTURE-PC 1.1, Reactor Analysis System with Sensitivity and Burnup
International Nuclear Information System (INIS)
2002-01-01
the addition of several sample problems, a new Windows executable, and a new Linux version. 2 - Methods:The VENTURE module applies the finite-difference diffusion or a simple P1 approximation. VENTURE uses an outer-inner iteration scheme with several different data handling methods. Over-relaxation is applied to the inner and outer iterations, and succeeding flux iterates may be accelerated with the Chebychev process. The BURNER code uses a difference formulation based on average generation rates, or a matrix exponential formulation, to approximate the solution of the coupled burnup differential equations, or an explicit solution for simply coupled nuclide chains. Space-dependence is included by working with zone averaged fluxes. The first user input data line must be the control module name used for the run. Venture-PC reads these data in CCCC ISOTXS format. AMPX working format libraries can be translated to ISOTXS format using the CONTAC module of AMPX-77. Alternately PSR-286/COMBINE-PC can be used to process ISOTXS data. 3 - Restrictions on the complexity of the problem: The executable is limited to a core container of 3,000,000 words, but it can be recompiled for much larger sizes due to the flat memory model of the Lahey Fortran 90 32-bit compiler. Prior versions of the code were unable to solve large mesh problems because of LF90 compiler limits on binary record lengths (<32,767 bytes). These records now are blocked, eliminating this restriction on problem size. Binary records created by the Fortran 95 compiler have a revised format from that created by the Fortran 90 compiler, in order to address a much larger record size limit. Pre-existing binary files written by any code compiled under Fortran 90 cannot be read by the code compiled under Fortran 95. Such files must be converted from 90 to 95 and vice-versa using Lahey-supplied tools that come with the compiler
Magnetic spectral signatures in the Earth's magnetosheath and plasma depletion layer
Anderson, Brian J.; Fuselier, Stephen A.; Gary, S. Peter; Denton, Richard E.
1994-01-01
Correlations between plasma properties and magnetic fluctuations in the sub-solar magnetosheath downstream of a quasi-perpendicular shock have been found and indicate that mirror and ion cyclotronlike fluctuations correlate with the magnetosheath proper and plasma depletion layer, respectively (Anderson and Fueselier, 1993). We explore the entire range of magnetic spectral signatures observed from the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE)spacecraft in the magnetosheath downstream of a quasi-perpendicular shock. The magnetic spectral signatures typically progress from predominantly compressional fluctuations,delta B(sub parallel)/delta B perpendicular to approximately 3, with F/F (sub p) less than 0.2 (F and F (sub p) are the wave frequency and proton gyrofrequency, respectively) to predominantly transverse fluctuations, delta B(sub parallel)/delta B perpendicular to approximately 0.3, extending up to F(sub p). The compressional fluctuations are characterized by anticorrelation between the field magnitude and electron density, n(sub e), and by a small compressibility, C(sub e) identically equal to (delta n(sub e)/n(sub e)) (exp 2) (B/delta B(sub parallel)) (exp 2) approximately 0.13, indicative of mirror waves. The spectral characteristics of the transverse fluctuations are in agreement with predictions of linear Vlasov theory for the H(+) and He(2+) cyclotron modes. The power spectra and local plasma parameters are found to vary in concert: mirror waves occur for beta(s ub parallel p) (beta (sub parallel p) identically = 2 mu(sub zero) n(sub p) kT (sub parallel p) / B(exp 2) approximately = 2, A(sub p) indentically = T(sub perpendicular to p)/T(sub parallel p) - 1 approximately = 0.4, whereas cyclotron waves occur for beta (sub parallel p) approximately = 0.2 and A(sub p) approximately = 2. The transition from mirror to cyclotron modes is predicted by linear theory. The spectral characteristics overlap for