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At least 757 records · Page 42

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NASA NTRS2010

Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems

In previous work, the authors documented the Multicomponent Ablation Thermochemistry (MAT) and Fully Implicit Ablation and Thermal response (FIAT) programs. In this work, key features from MAT and FIAT were combined to create the new Fully Implicit Ablation, Thermal response, and Chemistry (FIATC) program. FIATC is fully compatible with FIAT (version 2.5) but has expanded capabilities to compute the multispecies surface chemistry and ablation rate as part of the surface energy balance. This new methodology eliminates B' tables, provides blown species fractions as a function of time, and enables calculations that would otherwise be impractical (e.g. 4+ dimensional tables) such as pyrolysis and ablation with kinetic rates or unequal diffusion coefficients. Equations and solution procedures are presented, then representative calculations of equilibrium and finite-rate ablation in flight and ground-test environments are discussed.

Milos, Frank S.↗

DOE OSTI2017

Sensitivity Coefficients for Diffusion Coefficients and Other Reactor Physics Parameters using CE TSUNAMI-3D

The TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation) capabilities within the SCALE code system leverage sensitivity coefficients for many criticality safety applications, including quantifying the data-induced uncertainty in the eigenvalue of critical systems, quantifying computational biases, and selecting applicable benchmark experiments. TSUNAMI sensitivity and uncertainty analysis tools have traditionally been limited to criticality safety application spaces, but the introduction of Generalized Perturbation Theory (GPT) sensitivity methods by Jessee in 2009 and Perfetti in 2013 has extended the scope of SCALE adjoint-weighted sensitivity and uncertainty analysis to include reactor physics applications. The continuous-energy (CE) TSUNAMI-3D GPT sensitivity analysis methods were originally developed to calculate sensitivity coefficients for a limited number of reaction-rate responses using CE Monte Carlo methods. These tools were recently applied in an Oak Ridge National Laboratory (ORNL)-directed research and development project to improve the efficiency of {sup 252}Cf production in the High Flux Isotope Reactor (HFIR) by understanding the sensitivity of key heavy actinide capture-to- fission ratios to potential system design changes. This work further extends the applicability of the CE TSUNAMI- 3D GPT methods to reactor physics applications by enabling the calculation of sensitivity coefficients for an expanded set of reaction rate responses-including a first-ever capability for conducting sensitivity analysis of neutron diffusion coefficients.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

Extension of the DIF3D Code for Molten Salt Reactor Analysis

The molten salt reactor (MSR) with the fuel dissolved into the liquid salt has been selected as one of the six Generation-IV reactors due to its excellent characteristics in the aspects of sustainability, economy, passive safety, and resource utilization. In a MSR, the fuel salt is circulated throughout the whole system and thus some of delayed neutron precursors generated in the core decay in position of low importance or even out of the core. As a result, the multiplication factor (k-eff) of MSR is smaller than that of a reactor of stationary fuel when all the other conditions are same. Therefore, the neutronics code developed for stationary fuel cannot be applied directly to MSR analysis. In this paper, we describe the extension and application of the DIF3D code to MSR neutronics analysis. The DIF3D code system is a multi-group steady-state neutron diffusion and transport theory solver. It provides three flux solution options: finite-difference diffusion theory, nodal diffusion theory, and variational nodal transport theory methods. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted. The DIF3D code has recently been modified to model the flowing fuel. To verify the new capability of DIF3D, the MSFR [4] core was analyzed with a wide range of velocity field of fuel salt and time spent outside of the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1976

The partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasilinear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient D sub Mu Mu for particles interacting with slab model magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field. Results are compared with those of quasilinear theory and also with those of Monte Carlo calculations. The major effect of the nonlinear treatment in this illustration is the determination of D sub Mu Mu in the vicinity of 90 deg pitch angles where quasilinear theory breaks down. The spatial diffusion coefficient parallel to a mean magnetic field is evaluated using D sub Mu Mu as calculated by this technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and is hence not a perturbation theory.

Jones, F. C.↗

NASA NTRS1985

Long-time asymptotics of a system for plasma diffusion

A system of parabolic nonlinear equations that describe the diffusion of a fully collisional plasma across a strong magnetic field is discussed. It is demonstrated that the solution to this system tends to a time asymptotic state which is of space-time separable form, theta(t)f(x). Furthermore, f(x) is independent of the initial conditions and theta(t) depends slightly on the initial conditions. The rate of decay of the temporal part is governed by a nonlinear eigenvalue problem. Since the equations are considered in a bounded domain we are able to analyze the effect of boundary conditions on the evolution of the system. Additional effects on radiation, heating, and particle injection can also be accounted for. Essential differences between the behavior of a fully-coupled system and a scalar equation are observed.

Rosenau, P.↗

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.↗

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 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↗

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 OSTI2018

Oxygen Reduction on Stainless Steel in Concentrated Chloride Media

In this work, a rotating disk electrode was used to measure the cathodic kinetics on stainless steel as a function of diffusion layer thickness (6 to 60 pm) and chloride concentration (0.6 to 5.3 M NaCl). It was found that while the cathodic kinetics followed the Levich equation for large diffusion layer thicknesses, the Levich equation over predicts the mass-transfer limited current density for diffusion layer thicknesses less than 20 Am. Also, an unusual transitory response between the activation and mass-transfer controlled regions was observed for small diffusion layer thicknesses that was more apparent in lower concentration solutions. The presence and reduction of an oxide film and a transition in the oxygen reduction mechanism were identified as possible reasons for this response. The implications of these results on atmospheric corrosion kinetics under thin electrolyte layers is discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Topological Hall effect in diffusive ferromagnetic thin films with spin-flip scattering

In this paper, we study the topological Hall (TH) effect in a diffusive ferromagnetic metal thin film by solving a Boltzmann transport equation in the presence of spin-flip scattering. A generalized spin-diffusion equation is derived which contains an additional source term associated with the gradient of the emergent magnetic field that arises from skyrmions. Because of the source term, spin accumulation may build up in the vicinity of the skyrmions. This gives rise to a spin-polarized diffusion current that in general suppresses the bulk TH current. Only when the spin-diffusion length is much smaller than the skyrmion size does the TH resistivity approach the value derived by Bruno et al. [Phys. Rev. Lett. 93, 096806 (2004)]. Finally, we derive a general expression of the TH resistivity that applies to thin-film geometries with spin-flip scattering, and show that the corrections to the TH resistivity become large when the size of room temperature skyrmions is further reduced to tens of nanometers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗