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Results for “KINETIC EQUATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Diffusivity in turbulent fluid containing two dominant scales, and compressible shear layer according to a kinetic theory

The solution of the two nonequilibrium-degree kinetic equation was first determined for the effective length scale and turbulence energy for a spatially homogeneous turbulence field with two characteristic length scales, where the source for one family of eddies exists. This solution was applied to the evaluation of the eddy diffusivity in the combustion chamber of an internal combustion engine. The result was compared with another existing solution. This was carried out to demonstrate the feasibility of obtaining an effective length-scale equation within the context of the kinetic theory. A formulation and partial solution of the compressible plane shear layer are also presented.

Chung, P. M.↗
NASA NTRS1982

Coupled hydromagnetic wave excitation and ion acceleration upstream of the earth's bow shock

A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.

Lee, M. A.↗
DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗
DOE OSTI2023

Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.

neoclassical transport↗
DOE OSTI2022

Development of a point kinetics subroutine for Molten Salt reactors in RELAP5-3D

RELAP5-3D has historically focused on accurate modeling of design-basis and beyond-design-basis accidents in solid fuel light-water reactors. The assumption used in solid fuel reactors that delayed neutron precursors remain at the location in which they were produced is inherently incorrect for a molten salt reactor with flowing fuel. Therefore, new methods for modeling MSR kinetics were required. Subroutine used in RELAP5-3D were updated to analyze point kinetics in a molten salt reactor during both steady state and transient analyses. The phenomena related to MSR kinetics that were added to RELAP5-3D include arrays to store previous values for independent and dependent variables, arrays to add terms to existing kinetics equations, and a new reactivity bias term. A custom MATLAB assessment code was used to establish a suite of verification tests. This capability is undergoing final documentation and testing for public release with a future version of RELAP5-3D.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stability margin analysis of the Holos-quad microreactor design

A simplified point model of the Holos-Quad microreactor is introduced. The model is based on the point kinetics equations coupled to three heat balance equations, representing the mean temperatures of the fuel particles, the graphite moderator and the helium coolant. The differential equations are converted to the frequency domain, enabling the construction of the closed-loop reactor transfer function. Using this function the stability margins of the core design is analyzed for various power levels. It is shown that the gain margins approaches infinity, demonstrating the stability of the reactor for all power levels. The phase margin at nominal power is about 60 degrees, however it shows a non-monotonous dependence on power, with minimal value obtained for about 10% of nominal power. As power level is further increased, the phase margin also increases, demonstrating the reactor becomes more stable. This behavior may be of high importance in load-follow scenarios, where the power level of the reactor changes with time. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Inferring small-sample-reactivity worth from oscillation experiment with auto-corrected local flux

To estimate reactivity changes as a function of time from the signal of detectors count rates, one usually uses point kinetic equations. However, when detectors are located inside the core, it is often necessary to compute a correction factor to account for the flux-shape deformation (i.e. the change of detector efficiency that may have been induced by neutron absorbers movements). Various simulation methods have been developed depending on transients observed. They range from the resolution of static equations up to full-time-dependent neutron transport in 3D. However, those methods require high computational-cost calculations of local reaction rates that rely on nuclear data evaluations. Therefore, a 'measured' reactivity is never determined through pure measurements. Taking advantage of the known oscillation movement of a small sample at the center of the MINERVE reactor, the innovative algorithm presented in this paper derives the correction factor needed to get no time drift on reactivity steps. Derived correction factors are in good agreement with those obtained independently with TRIPOLI-4 through sensitivity analysis. Low sensitivity to the sample composition and moderate sensitivity to the detectors position reinforce the reliability of those results. This application paves the way to almost pure nuclear data reactivity measurements. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Transport and kinetics properties of LaF 3 in FLiNaK molten salt determined by electrochemical methods

It is found that lanthanum species can exist in the form of LaF 6 3- in FLiNaK (46.5 LiF-11.5 NaF-42 KF, mol%) molten salt in previous studies. The understanding of transport and reaction kinetics parameters of LaF 6 3- ions in FLiNaK molten salt is essential for the electrochemical separation of lanthanum from FLiNaK melt to achieve the coolant clean-up in fluoride salt cooled high-temperature reactor (FHR). Through conducting chronopotentiometry tests, the diffusion coefficients of LaF 6 3- ions in FLiNaK molten salt at the temperature range of 923 K–1023 K were determined. By conducting potentiodynamic polarization measurements at different concentrations and temperatures, the exchange current density, reaction rate constant, and charge transfer coefficient were obtained. The experiment data of potentiodynamic polarization were analyzed using a non-simplified electrode kinetics equation which incorporates both mass transfer and reaction kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Study of Alfvén eigenmode stability in Quasi-Poloidal Stellarator (QPS) plasma using a Landau closure model

The aim of this study is to analyze the linear stability of Alfvén eigenmodes (AE) in the QPS device heated by a tangential neutral beam injector (NBI). The analysis is performed using the gyro-fluid code FAR3d, that solves the reduced MHD equations for the thermal plasma coupled with moments of the kinetic equation for the energetic particles (EP). The AE stability is calculated in several operational regimes of the tangential NBI: EP β between 0.001 and 0.1, EP energy between 12 and 180 keV and different radial locations of the beam. The analysis is performed for vacuum and finite β equilibria as well as QPS configurations with two and three periods. The EP β threshold in the vacuum case is 0.001 and the AE frequency is lower as the energy of the EP population decreases. Toroidal Alfvén eigenmodes with f = 80–120 kHz and elliptical AE between f = 120–350 kHz are triggered between the middle-outer plasma region ($r/a \gt 0.5$). The AE stability improves in the simulations with finite β equilibria and three period configurations with respect to the vacuum case with two periods because the continuum gaps are slender, leading to a higher threshold of the EP β, above 0.03 for the AEs triggered by the helical mode families. Helical effects are not strong enough to destabilize Helical Alfvén eigenmodes, the AEs with the largest growth rates are triggered by the n = 1 and n = 2 toroidal families.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1973

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration-vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is then discussed.

Lind, R. C.↗
DOE OSTI2021

Lagrangian particle model for 3D simulation of pellets and SPI fragments in tokamaks

A 3D numerical model for the ablation of pellets and shattered pellet injection (SPI) fragments in tokamaks in the plasma disruption mitigation and fueling parameter space has been developed based on the Lagrangian particle code [R. Samulyak, X. Wang, H.-S. Chen, Lagrangian Particle Method for Compressible Fluid Dynamics, J. Comput. Phys., 362 (2018), 1-19]. The pellet code implements the low magnetic Reynolds number MHD equations, kinetic models for the electronic heating, a pellet surface ablation model, an equation of state that supports multiple ionization states, radiation, and a model for grad-B drift of the ablated material across the magnetic field. The Lagrangian particle algorithm is highly adaptive, capable of simulating a large number of fragments in 3D while eliminating numerical difficulties of dealing with the tokamak background plasma. The code has achieved good agreement with theory for spherically symmetric ablation flows. Axisymmetric simulations of neon and deuterium pellets in magnetic fields ranging from 1 to 6 Tesla have been compared with previous simulations using the FronTier code, and very good agreement has also been obtained. Furthermore, the main physics contribution of the paper is a detailed study of the influence of 3D effects, in particular grad-B drift, on pellet ablation rates and properties of ablation clouds. Smaller reductions of ablation rates in magnetic fields compared to axially symmetric simulations have been demonstrated because the ablated material is not confined to narrowing channels in the presence of grad-B drift. Contribution of various factors in the grad-B drift model has also been quantified.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Carbon-Carbon Aeroshell Chemical Reaction Model in an Open RPS in Martian Environment

A new RPS is being designed to be open to the vacuum of space to improve its thermal efficiency during deep space missions. This design, however, could lead to some potential complications if it is ever used in the low-pressure gas environment of mission destinations like Mars. This report documents the development of a chemical kinetics reaction model of the FWPF carbon-carbon aeroshell in the Martian gaseous environment. This model uses an “infinite sink” assumption where the RPS is open to the Martian environment with open exchange of flowing gases, so the gas chemistry over the aeroshell does not change with the reaction and represents the worst case scenario of the chemical reaction of the FWPF in the Martian environment. The model combines the kinetics equation of both oxidation reactions that would occur on Mars: the Langmuir-Hinshelwood kinetics of the Boudouard reaction of CO 2 with the chemical kinetics of O 2 oxidation of the carbon-carbon. The FWPF chemical reaction model was benchmarked using the Opila’s experimental chemical reaction test data (1) in a simulated Martian environment to increase the validity of the model’s predicted mass loss rate. The output of the benchmarked chemical reaction model showed a trade-off between the maximum temperature of the aeroshell to have less than 10% reaction at the mission life. For example, an RPS with a five-year intended mission life on Mars has a maximum aeroshell temperature of 835 K / 562 °C, increasing the mission life to ten years reduces the maximum operating temperature to 810 K / 527 °C. If the aeroshell operating temperature in the new RPS on the surface of Mars is 960 Kelvin, the model calculates that the life is limited to 0.22 years / 81 days. Increasing the aeroshell temperature to 1343 Kelvin, further reduces the life to 0.375 days / 9 hrs. This illustrates the thermally activated nature of the chemical kinetics model in limiting the life of the aeroshell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Carbon-Carbon Aeroshell Chemical Reaction Model in an Open RPS in Martian Environment

A new RPS is being designed to be open to the vacuum of space to improve its thermal efficiency during deep space missions. This design, however, could lead to some potential complications if it is ever used in the low-pressure gas environment of mission destinations like Mars. This report documents the development of a chemical kinetics reaction model of the FWPF carbon-carbon aeroshell in the Martian gaseous environment. This model uses an “infinite sink” assumption where the RPS is open to the Martian environment with open exchange of flowing gases, so the gas chemistry over the aeroshell does not change with the reaction and represents the worst case scenario of the chemical reaction of the FWPF in the Martian environment. The model combines the kinetics equation of both oxidation reactions that would occur on Mars: the Langmuir-Hinshelwood kinetics of the Boudouard reaction of CO2 with the chemical kinetics of O2 oxidation of the carbon-carbon. The FWPF chemical reaction model was benchmarked using the Opila’s experimental chemical reaction test data (1) in a simulated Martian environment to increase the validity of the model’s predicted mass loss rate. The output of the benchmarked chemical reaction model showed a trade-off between the maximum temperature of the aeroshell to have less than 10% reaction at the mission life. For example, an RPS with a five-year intended mission life on Mars has a maximum aeroshell temperature of 835 K / 562 °C, increasing the mission life to ten years reduces the maximum operating temperature to 810 K / 527 °C. If the aeroshell operating temperature in the new RPS on the surface of Mars is 960 Kelvin, the model calculates that the life is limited to 0.22 years / 81 days. Increasing the aeroshell temperature to 1343 Kelvin, further reduces the life to 0.375 days / 9 hrs. This illustrates the thermally activated nature of the chemical kinetics model in limiting the life of the aeroshell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗