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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Comparison of subchannel and averaged channel thermal-hydraulic descriptions on coupled pin-by-pin neutronic calculations

Best-estimate transient analysis of Light Water Reactors (LWRs) requires high accuracy code systems solving neutronics (NK), thermal-hydraulics (TH) and thermal-mechanics to model the core behavior. For long time, nodal diffusion methods for solution of the transport equation using assembly size computational meshes have been applied neglecting the details within the fuel assembly, or using 'pin power reconstruction' techniques to predict those details. Moreover, the multiphysics analysis has been commonly performed coupling those neutronic diffusion methods to thermal-hydraulic system codes using a nodalization of several fuel assemblies per computational node without taking into account the effects that this type of averaging can have on the results obtained. This paper presents the work accomplished with the coupled system COBAYA4/CTF for a preliminary analysis of the effect of the different accuracy levels in the NK and TH domain. COBAYA4 is a neutronic code able to solve the diffusion equation at two resolution levels, nodal and pin by pin (PbP). CTF is a thermo-hydraulic code able to solve the coolant conservation equations also at two levels, channel (fuel assembly averaged solution) and sub-channel (real cooling channel) level. The coupled system COBAYA4/CTF is used through SALOME platform, i.e. SALOME is the software able to map conveniently the NK and TH meshes. This coupling allows combining different resolution levels for NK and TH problems. Therefore, the study of the effect of using different resolutions for the NK and TH nodalizations has been performed applying the system to a fuel assembly with selected boundary conditions. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1984

Formation and dynamics of large-scale magnetic structures in the ionosphere of Venus

The formation and dynamics of large-scale magnetic structures in the ionosphere of Venus are examined. It is shown that such structures must be the result of steady state convection of interplanetary field lines into the ionosphere by the small amount of solar wind plasma (less than or approximately equal to 1-5 percent) absorbed by the planetary atmosphere below the ionopause, rather than isolated remnants of large fields persisting for long periods without connection to the solar wind induced current and convection pattern. In particular, it is demonstrated that the magnetic diffusion of such structures would result in their dissipation with time scales of 1-10 min, if they were not steady state structures in convective and diffusive equilibriuim. It is shown that the equations governing the diffusion of these magnetic structures are similar to those governing diffusion of a gas out of an enclosed chamber with a porous wall, and a simple analog is illustrated. The application of these results to magnetic fields of astrophysical plasmas is discussed.

Cloutier, P. A.↗
NASA NTRS1972

Relation of the diffuse reflectance remission function to the fundamental optical parameters.

The Kubelka-Munk equations describing the diffuse reflectance of a powdered sample were compared to equations obtained using a uniformly-sized rough-surfaced spherical particle model. The comparison resulted in equations relating the remission function and the Kubelka-Munk constants to the index of refraction, the absorption coefficient, and the average particle diameter of a powdered sample. Published experimental results were used to test the equation relating to the remission function to the fundamental optical parameters.

Simmons, E. L.↗
DOE OSTI2015

Modeling weakly-ionized plasmas in magnetic field: A new computationally-efficient approach

Despite its success at simulating accurately both non-neutral and quasi-neutral weakly-ionized plasmas, the drift-diffusion model has been observed to be a particularly stiff set of equations. Recently, it was demonstrated that the stiffness of the system could be relieved by rewriting the equations such that the potential is obtained from Ohm's law rather than Gauss's law while adding some source terms to the ion transport equation to ensure that Gauss's law is satisfied in non-neutral regions. Although the latter was applicable to multicomponent and multidimensional plasmas, it could not be used for plasmas in which the magnetic field was significant. This paper hence proposes a new computationally-efficient set of electron and ion transport equations that can be used not only for a plasma with multiple types of positive and negative ions, but also for a plasma in magnetic field. Because the proposed set of equations is obtained from the same physical model as the conventional drift-diffusion equations without introducing new assumptions or simplifications, it results in the same exact solution when the grid is refined sufficiently while being more computationally efficient: not only is the proposed approach considerably less stiff and hence requires fewer iterations to reach convergence but it yields a converged solution that exhibits a significantly higher resolution. The combined faster convergence and higher resolution is shown to result in a hundredfold increase in computational efficiency for some typical steady and unsteady plasma problems including non-neutral cathode and anode sheaths as well as quasi-neutral regions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2018

Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. I: Approach Based on the Far-Field Foldy Equations

In this paper, we revisit, with further enhancements and clarifications, the self-consistent first-principles approach developed previously for deriving the vector radiative transfer theory for a discrete random medium with a sparse concentration of particles. We specifically consider the case of a plane-parallel particulate layer embedded in an otherwise homogeneous unbounded medium. The solution method is based on the far-field Foldy equations, an order-of-scattering expansion for the total field derived under the Twersky approximation, the computation of the coherent field by assuming that the positions of the particles are uncorrelated, and the ladder approximation for the coherency dyadic. The latter yields an integral equation for the diffuse specific coherency dyadic, defined through an angular spectrum repre- sentation for the coherency dyadic, which in turn, gives the vector radiative transfer equation for the diffuse specific intensity column vector. We analyze specifically the computation of the coherent field for inhomogeneous particulate media and multiple species of particles, the continuous extension of the far-field representation to the near field, the Foldy approximation, and the Foldy integral equation for the coherent field. Finally, we discuss the transition from the vector to the scalar radiative transfer equation.

Doicu, Adrian↗
DOE OSTI2022

Kinetic Model for Moisture-Controlled CO 2 Sorption

The understanding of the sorption/desorption kinetics is essential for practical applications of moisture-controlled CO 2 sorption. We introduce an analytic model of the kinetics of moisture-controlled CO 2 sorption and its interpretation in two limiting cases. In one case, chemical reaction kinetics on pore surfaces dominates, in the other case, diffusive transport through the sorbent defines the kinetics. Here, we show that reaction kinetics, which is dominant in the first case, can be expressed as a linear combination of 1st and 2nd order kinetics in agreement with the static isotherm equation derived and validated in a previous paper. The interior transport kinetics can be described by non-linear diffusion equations. By combining all carbon species into a single equation, we can eliminate — in certain limits — the source terms associated with chemical reactions. In this case, the governing equation is ∂θ/∂t = –∇ · (–D eff ∇ θ ). For a sorbent in a form of a flat sheet or a membrane, one can maintain the same functional form of a diffusion equation by introducing a generalized effective diffusivity D M that combines contributions from both surface chemical reaction kinetics and interior diffusive transport kinetics. Experimental data of transient CO 2 flux in a preconditioned commercial anion exchange membrane fit well to the 1st order model as long as very dry states are avoided, validating the theory. The observed DM for a preconditioned commercial anion exchange membrane ranges from 6.6× 10 -14 to 7.1× 10 -14 m 2 s -1 at 35°C. These small values compared to typical ionic diffusivities imply a very slow kinetics, which will be the largest issue that needs to be addressed for practical application. The collected transient CO 2 flux data are used to predict the magnitude of a continuous CO 2 pumping flux in an active membrane that transports CO 2 against a CO 2 concentration gradient. The pumped CO 2 flux is supported by water flux due to a water concentration gradient.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

An efficient transport solver for tokamak plasmas

A simple approach to efficiently solve a coupled set of 1-D diffusion-type transport equations with a stiff transport model for tokamak plasmas is presented based on the 4th order accurate Interpolated Differential Operator scheme along with a nonlinear iteration method derived from a root-finding algorithm. Here, numerical tests using the Trapped Gyro-Landau-Fluid model show that the presented high order method provides an accurate transport solution using a small number of grid points with robust nonlinear convergence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems

We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Nonclassical Particle Transport in the 1-D Diffusive Limit

A nonclassical linear Boltzmann equation has been recently proposed to address nonexponential attenuation of the particle flux in certain inhomogeneous random media applications. In particular, this effect arises in Pebble Bed reactor cores, in which the locations of the pebbles are spatially correlated. In this paper, we investigate nonclassical particle transport taking place in a 1-D random periodic diffusive system. We provide computational results that validate the theoretical predictions, demonstrating for the first time that the solution of the nonclassical particle transport equation is well-approximated by the solution of the nonclassical diffusion equation. For simplicity, we consider the following assumptions: (i) transport occurs in rod geometry, in which particles can only move in the directions μ = ±1; (ii) transport is monoenergetic; and (iii) scattering is isotropic. This paper provides numerical results that demonstrate the validity of the nonclassical diffusion approximation to the nonclassical transport equation in certain 1-D diffusive systems. To our knowledge, this is the first time computational results that validate the predictions of the asymptotic theory for the nonclassical model are presented. This result provides a more solid foundation in which to improve this theory for relevant nuclear applications. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Finite-volume scheme for anisotropic diffusion

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A Study of the von Neumann Stability Analysis of a Semi-implicit Numerical Method Applied Over the Radial Impurity Transport Equation in Tokamak Plasma

The radial impurity transport equation for tokamak plasma is a form of diffusion–convection–reaction equation. The impurity transport equation is solved to determine the distribution of impurity (non-fuel) ion species with different ionization states perpendicular to magnetic surfaces of tokamak plasma. The equation for each charge (ionization) state Z is a non-linear, second-order in space, first-order in time, parabolic partial differential equation coupled to the previous Z − 1 and the next Z + 1 charge states of the impurity species through its reaction term. The number of differential equations to be solved simultaneously is hence determined by the number of ionization states of the impurity species studied. The solution to the set of these coupled equations can be obtained using a semi-implicit numerical method applied on it. The present study describes the application of von Neumann stability analysis over the semi-implicit numerical method applied over the radial impurity transport equation and determines a generic stability criterion for the method. The stability analysis is further illustrated using the geometry of Aditya tokamak installed at the Institute for Plasma Research Gandhinagar, India as an example. The impurity species considered is oxygen (Atomic number = 8). This leads to a set of eight coupled equations for charge states Z = 1 to 8 over which von Neumann analysis is illustrated in present study.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1998

Multi-Component Diffusion with Application To Computational Aerothermodynamics

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

Sutton, Kenneth↗
DOE OSTI2015

Biocellion Version 2.0

This work extends Biocellion 1.0 to solve advection-reaction-diffusion and incompressible Navier-Stokes partial differential equations to model water/blood flow. Biocellion is a software framework to simulate a large number of cells using high-performance parallel computers. The version 1.0 allows software users to describe biological system behaviors as a set of rules describing how individual cells behave and how cells locally interact with neighboring cells or the surrounding micro-environment. However, the version 1.0 does not support users to incorporate water/blood flow into the model, which is important to properly capture long distance communications between distant cells. This extension (version 2.0) integrates two partial differential equation solvers to the Biocellion framework to solve this limitation. Navier-Stokes equation solvers (for incompressible flow) are added to compute flow rate, and advection-reaction-diffusion equation solvers are added to update molecular concentrations considering both advection (due to flow) and local diffusion.

Kang, Seunghwa↗
NASA NTRS1977

The relative diffusion of strong magnetic fields and tenuous gases

General equations are given for treating the diffusion of a magnetic field in a fluid with electrical conductivity and a resistive diffusion coefficient. Consequences of nonnegligible gas motion are investigated by considering the one-dimensional problem where a tenuous isothermal gas with pressure expressed as a function of x-coordinate and time is enmeshed in a magnetic field in the y-direction. Approximate equations are obtained for the case of weak fluctuations in gas or field pressure, and the properties of a nonlinear diffusion equation are illustrated with the example of an initial thin slab of gas confined by a uniform field on either side. The advance of a gas front into a nonvanishing gas density is illustrated by using the progressive wave solution. Application of the results to the evolution of streamers and filaments observed in the solar corona is briefly discussed

Parker, E. N.↗
DOE OSTI2015

Predicting X-ray diffuse scattering from translation–libration–screw structural ensembles

A method of simulating X-ray diffuse scattering from multi-model PDB files is presented. Despite similar agreement with Bragg data, different translation–libration–screw refinement strategies produce unique diffuse intensity patterns. Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier’s equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation–libration–screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls-as-xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Discontinuous diffusion synthetic acceleration for S{sub n} transport on 2D arbitrary polygonal meshes

In this paper, a Diffusion Synthetic Acceleration (DSA) technique applied to the S{sub n} radiation transport equation is developed using Piece-Wise Linear Discontinuous (PWLD) finite elements on arbitrary polygonal grids. The discretization of the DSA equations employs an Interior Penalty technique, as is classically done for the stabilization of the diffusion equation using discontinuous finite element approximations. The penalty method yields a system of linear equations that is Symmetric Positive Definite (SPD). Thus, solution techniques such as Preconditioned Conjugate Gradient (PCG) can be effectively employed. Algebraic MultiGrid (AMG) and Symmetric Gauss–Seidel (SGS) are employed as conjugate gradient preconditioners for the DSA system. AMG is shown to be significantly more efficient than SGS. Fourier analyses are carried out and we show that this discontinuous finite element DSA scheme is always stable and effective at reducing the spectral radius for iterative transport solves, even for grids with high-aspect ratio cells. Numerical results are presented for different grid types: quadrilateral, hexagonal, and polygonal grids as well as grids with local mesh adaptivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Mutual diffusion of binary liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride

Mutual diffusion coefficients of all 20 binary liquid mixtures that can be formed out of methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon tetrachloride without a miscibility gap are studied at ambient conditions of temperature and pressure in the entire composition range. The considered mixtures show a varying mixing behavior from almost ideal to strongly non-ideal. Predictive molecular dynamics simulations employing the Green-Kubo formalism are carried out. Radial distribution functions are analyzed to gain an understanding of the liquid structure influencing the diffusion processes. It is shown that cluster formation in mixtures containing one alcoholic component has a significant impact on the diffusion process. The estimation of the thermodynamic factor from experimental vapor-liquid equilibrium data is investigated, considering three excess Gibbs energy models, i.e., Wilson, NRTL, and UNIQUAC. It is found that the Wilson model yields the thermodynamic factor that best suits the simulation results for the prediction of the Fick diffusion coefficient. Four semi-empirical methods for the prediction of the self-diffusion coefficients and nine predictive equations for the Fick diffusion coefficient are assessed and it is found that methods based on local composition models are more reliable. Finally, the shear viscosity and thermal conductivity are predicted and in most cases favorably compared with experimental literature values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order S{sub N} Equations in Near-Void Regions

The common definition of the diffusion coefficient as the inverse of three times the transport cross section is not compatible with voids. Morel introduced a non-local tensor diffusion coefficient that remains finite in voids. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coefficient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction. It was demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors have been applied to modeling the TREAT reactor confirming the findings of Larsen and Trahan. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S{sub N} equations discretized with the discontinuous finite element method (DFEM). This NDA method uses a scalar diffusion coefficient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it suffers from very large and potentially unbounded diffusion coefficients in the low order problem. However, it was noted that the choice of the diffusion coefficient does not influence consistency of the method at convergence and hence the diffusion coefficient is essentially a free parameter. The choice of the diffusion coefficient does, however, affect the convergence behavior of the nonlinear diffusion iterations. Within this work we use Morel's non-local diffusion coefficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant enhancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coefficients, the periodical horizontal interface problem is used. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗