Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

INITIAL EXPLORATION OF A NOVEL TRANSIENT ARREST SYSTEM INVOLVING FUEL HEATING (Presentation)

A preliminary analysis on a novel accident response system to diminish the severity of supercritical transients was conducted. The novel accident response system, called the instant shock arrest system, involves using electricity to heat the nuclear fuel at the onset of a large accidental reactivity insertion. This system is specifically designed for reactors with metallic fuel, such that the fuel is capable of conducting electricity, and being resistively heated. A reactor dynamics model of the advanced test reactor was created using the point kinetics equations and a linear reactivity feedback model to simulate how the system would effect the maximum fuel temperatures experienced during the transient. Transients with the instant shock arrest system were compare to those without it. It was found that the instant shock arrest system initially heated the fuel more than the unaffected transient but the negative reactivity inserted from such heating was enough to lower the maximum fuel temperature experienced during the transient. After simulating six different accident scenarios with reactivity insertions ranging from 0.5 \$ to 1.3 \$, it was found that the an optimal system response could reduce peak fuel temperatures during the transient by 3.5% to 5%. Furthermore, discussion was given on how the optimal system response could be obtained using relatively simple numerical optimization algorithms due to the smoothness of the optimization problem.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Development for Integrated System-Level Analysis Capabilities in SAM for Molten Salt Reactors

In recent years, there has been renewed interest in Molten Salt Reactors (MSRs) for their potential advantages compared to reactors that rely on solid fuel. In response to such interest, many methods and codes have been developed to capture the unique features of MSRs. Among them, the System Analysis Module (SAM) is a modern system analysis tool that provides fast-running, modest-fidelity, whole-plant transient analysis capabilities, essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. For liquid-fuel MSRs, the complex physics and chemistry involved in MSR operation—such as reactor kinetics, fluid flow, heat transfer, and salt composition dynamics—pose significant challenges for system-level modeling. Specific modeling capabilities are needed for system-level transient simulation. This paper presents recent advancements in SAM capability enhancements for system-level modeling of MSRs, focusing on improved simulation fidelity, computational efficiency, and multi-physics integration. Key enhancements include the development of species transport, Delayed Neutron Precursor (DNP) drift, modified Point Kinetics Equations (PKE), decay heat modeling, key fission product behavior, salt corrosion, and thermal-hydraulic coupling, as well as code robustness and performance enhancements for MSR applications. The code enhancement allows for better predictive accuracy in safety analysis, transient behavior, and operational optimization, thus supporting the design and licensing of next-generation MSRs. Results from case studies are presented to demonstrate the benefits of these enhancements in accurately capturing key reactor transient behaviors.

Hu, Rui (ORCID:0000000237712920)↗
DOE OSTI2022

PolyODENet: Deriving mass-action rate equations from incomplete transient kinetics data

Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space. Here, using simple catalytic reaction models, we demonstrate that PolyODENet can predict reaction profiles of unknown species and doing so even reveal hidden parts of reaction mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data for Catalyst and Reactor Design Considerations for Selective Production of Acids by Oxidative Cleavage of Alkenes with H2O2

Oxidative cleavage of alkenes and unsaturated fatty acids with hydrogen peroxide gives an efficient and sustainable process to obtain mono- and di-acids for polymers and lubricants with fewer safety risks and less environmental impact than processes that utilize ozone or other inorganic oxidizers (e.g., permanganate, dichromate, etc.). Guided by insight into the mechanisms for competing reaction pathways (i.e., epoxidation of alkene on W–(η2-O2) complexes vs. H2O2 decomposition) and the apparent kinetics derived from kinetic experiments, here, we postulate that W-based heterogeneous catalysts can provide high performance and stable operations at low H2O2 concentrations. Semi-batch reactors with continuous introduction of H2O2 solutions offer the means to maintain low H2O2 concentrations while providing sufficient quantities of H2O2 to satisfy the reaction stoichiometry. We derived simple kinetic model equations for the epoxidation, ring-opening, oxidative cleavage, and oxidation steps and fit theses equations to batch experimental data to obtain kinetic parameters. This kinetic model describes the concentration profiles of reactant, oxidant, and products well as shown by agreement with experimental data. Further predictions of the optimal H2O2 feed rate for semi-batch operation utilized by the proposed rate expressions and the reactor design equations suggest that low H2O2 feed rate increases selectivity towards oxidative cleavage products and selective use of H2O2 for oxidative cleavage pathway. Comparisons of oxidative cleavage of 4-octene in batch and semi-batch reactors show that semi-batch reactors with optimized molar feed rates of H2O2 increased oxidative cleavage product selectivities (76% to 99%; with an increase in butyric acid selectivity from 1% to 55%) and H2O2 selectivity (3% to 30%). In addition, semi-batch reaction conditions used avoid H2O2-mediated dissolution of W-atoms from the catalyst. Analysis of these findings suggest that solid oxide catalysts will be effective for continuous oxidative cleavage reactions if deployed within fixed-bed reactors that allow for distributed introduction of reactants and therefore low in situ concentrations of H2O2.

Catalysis↗
DOE OSTI2022

Catalyst and reactor design considerations for selective production of acids by oxidative cleavage of alkenes and unsaturated fatty acids with H 2 O 2

Oxidative cleavage of alkenes and unsaturated fatty acids with hydrogen peroxide gives an efficient and sustainable process to obtain mono- and di-acids for polymers and lubricants with fewer safety risks and less environmental impact than processes that utilize ozone or other inorganic oxidizers (e.g., permanganate, dichromate, etc.). Guided by insight into the mechanisms for competing reaction pathways (i.e., epoxidation of alkene on W–(η 2 -O 2 ) complexes vs. H 2 O 2 decomposition) and the apparent kinetics derived from kinetic experiments, here, we postulate that W-based heterogeneous catalysts can provide high performance and stable operations at low H 2 O 2 concentrations. Semi-batch reactors with continuous introduction of H 2 O 2 solutions offer the means to maintain low H 2 O 2 concentrations while providing sufficient quantities of H 2 O 2 to satisfy the reaction stoichiometry. We derived simple kinetic model equations for the epoxidation, ring-opening, oxidative cleavage, and oxidation steps and fit theses equations to batch experimental data to obtain kinetic parameters. Furthermore, this kinetic model describes the concentration profiles of reactant, oxidant, and products well as shown by agreement with experimental data. Further predictions of the optimal H 2 O 2 feed rate for semi-batch operation utilized by the proposed rate expressions and the reactor design equations suggest that low H 2 O 2 feed rate increases selectivity towards oxidative cleavage products and selective use of H 2 O 2 for oxidative cleavage pathway. Comparisons of oxidative cleavage of 4-octene in batch and semi-batch reactors show that semibatch reactors with optimized molar feed rates of H 2 O 2 increased oxidative cleavage product selectivities (76% to 99%; with an increase in butyric acid selectivity from 1% to 55%) and H 2 O 2 selectivity (3% to 30%). In addition, semibatch reaction conditions used avoid H 2 O 2 -mediated dissolution of W-atoms from the catalyst. Analysis of these findings suggest that solid oxide catalysts will be effective for continuous oxidative cleavage reactions if deployed within fixed-bed reactors that allow for distributed introduction of reactants and therefore low in situ concentrations of H 2 O 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Kinetic closures for unmagnetized and magnetized plasmas

Parallel and perpendicular closures with cyclotron resonance effects retained for the five-moment (density, temperature, and flow velocity) fluid equations are derived by solving the kinetic equation with the Bhatnagar–Gross–Krook operator in Fourier space. For parallel propagation, the parallel closures are reduced to those of Ji et al. [Phys. Plasmas 20, 082121 (2013)]. The closures when combined to the fluid equations reproduce the fully kinetic dispersion relation that can be directly derived from the kinetic equation. The closures for the five-moment fluid system can be utilized to derive closures for the extended fluid system, which is demonstrated by deriving closures for the ten-moment system consisting of density, flow velocity, temperature, and viscosity tensor equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Isomerization kinetics of azobenzene crosslinked to a liquid crystal polymer network

Azobenzene is an important chromophore having numerous applications that are a direct implication of its ability to change shape upon irradiation with a suitable wavelength. Here, in this study, photoisomerization kinetics of a diacrylate azobenzene molecule (A3MA) cross-linked to a liquid crystal polymer network (LCN) is investigated. Isomerization experiments were conducted on planar LCN thin films with varying cross-linking densities for a fixed azobenzene concentration. The experiments were conducted at approximately 26 °C, which is significantly below each film’s glass transition temperature. The forward trans-cis and reverse cis-trans isomerization slows down in crosslinked azobenzene liquid crystal polymer networks (ALCNs) as compared to a solution and an uncrosslinked polymer mixture. The observed slowdown is due to the reduction in the free volume and increased steric hindrances with an increase in crosslinking. A single-term first-order kinetics rate equation is known to describe the isomerization kinetics in solutions or uncrosslinked mixtures while the same form fails to represent the reaction kinetics in moderate to highly cross-linked ALCNs. Our results for the first time indicate that a two-term first-order reaction rate is an accurate way to describe the forward trans-cis and reverse thermal cis-trans isomerization in crosslinked azobenzene liquid crystal polymer networks. In addition, the effect of film thickness and incident intensities on the reaction kinetics is investigated. Finally, the two-term isomerization kinetics is incorporated into a finite element photo-chemo-mechanical model to reveal the consequent slowdown in the actuation response of ALCN films. The current findings will be of particular interest to theoreticians and experimentalists alike, for it will help predict and understand accurately the responses of azobenzene-based coatings, and actuators and may have potential applications in underwater soft robotics.

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

Advanced Turbulence Models for Large-Scale Atmospheric Boundary Layer Flows

We present high-fidelity large-eddy-simulation (LES) modeling approaches for the turbulent atmospheric boundary layer (ABL) flows. Wind energy is a prime example of an application driven by ABL. Generation of electrical energy from farms of wind turbines at night in the stable ABL is a particularly interesting situation. In this report, we consider the well-known GEWEX (Global Energy and Water Cycle Experiment) Atmospheric Boundary Layer Study (GABLS) stably stratified benchmark LES case. We use a high-order spectral element code Nek5000/RS, which is supported under the DOE's Exascale Computing Project (ECP) Center for Efficient Exascale Discretizations (CEED) project, targeting application simulations on various acceleration-device based exascale computing platforms. In our earlier ANL report, we demonstrated our newly developed subgrid-scale (SGS) models based on high-pass filter (HPF), mean-field eddy viscosity (MFEV), and Smagorinsky (SMG) with no-slip and traction boundary conditions, provided with low-order statistics, convergence and turbulent structure analysis. In this report, we extend the range of our SGS modeling approaches in the context of the mean-field eddy viscosity (MFEV), to include the solution of an SGS turbulent kinetic energy equation (TKE). We demonstrate the model fidelity of Nek5000/RS in comparison to that of AMR-Wind, a block-structured second-order finite-volume code with adaptive-mesh-refinement capabilities, with which we studied scaling performance for both codes in comparison on DOE's leadership computing platforms.

17 WIND ENERGY↗
DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗
DOE OSTI2023

Computational Materials Design for Ceramic Nuclear Waste Forms Using Machine Learning, First-Principles Calculations, and Kinetics Rate Theory

Ceramic waste forms are designed to immobilize radionuclides for permanent disposal in geological repositories. One of the principal criteria for the effective incorporation of waste elements is their compatibility with the host material. In terms of performance under environmental conditions, the resistance of the waste forms to degradation over long periods of time is a critical concern when they are exposed to natural environments. Due to their unique crystallographic features and behavior in nature environment as exemplified by their natural analogues, ceramic waste forms are capable of incorporating problematic nuclear waste elements while showing promising chemical durability in aqueous environments. Recent studies of apatite- and hollandite-structured waste forms demonstrated an approach that can predict the compositions of ceramic waste forms and their long-term dissolution rate by a combination of computational techniques including machine learning, first-principles thermodynamics calculations, and modeling using kinetic rate equations based on critical laboratory experiments. By integrating the predictions of elemental incorporation and degradation kinetics in a holistic framework, the approach could be promising for the design of advanced ceramic waste forms with optimized incorporation capacity and environmental degradation performance. Such an approach could provide a path for accelerated ceramic waste form development and performance prediction for problematic nuclear waste elements.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Benchmark of the KGMf with a coupled Boltzmann equation solver

The Kinetic Global Model framework (KGMf) is an open-source general-purpose global model (spatially averaged) simulation code developed to explore the reaction kinetics and pathways in plasma discharge systems. It contains species continuity and electron energy balance equations, with a time-dependent evaluated electron energy distribution function (EEDF) for electron impact reactions. The EEDF is utilized to determine the rate coefficients for electron impact reactions, which can have profound impact on the temporal evolutions of plasma parameters. Previously, the EEDF was commonly assumed as Maxwellian or an analytical function of the effective electron temperature. In this work, the KGMf is coupled with a Boltzmann equation (BE) solver to self-consistently compute the EEDF. The EEDF evolution frequency is determined based on relative changes of the reduced electric field. The KGMf is benchmarked with the ZDPlasKin code based on high-pressure low-temperature argon plasma discharge cases. Additionally, the temporal evolutions of reduced electric field, electron temperature, EEDF, reaction rates, and species densities, are obtained and compared under different discharge conditions, showing good agreement between the KGMf and the ZDPlasKin simulations. The application of the KGMf for predicting breakdown times in high power microwave discharges is also presented, which shows qualitative agreement with particle-in-cell simulations. The KGMf can be further applied for more complicated plasma discharge systems, where the reaction kinetics are more intricate (e.g., plasma-assisted combustion systems).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Pressure–Strain Interaction as the Energy Dissipation Estimate in Collisionless Plasma

The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure–strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure–strain interaction. The incompressive part of the pressure–strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov–Maxwell equations, a kinetic plasma approach, and the lag dependent von Kármán–Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation in estimating the dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure–strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Impact of nuclear reactor radiation on the performance of AlN/sapphire surface acoustic wave devices

The performance of an AlN/sapphire surface acoustic wave (SAW) delay line device was characterized in real time under irradiation inside a nuclear reactor. Both its resonant frequency and transmission efficiency were observed to respond to a change in reactor power. The response follows an exponentially saturating behavior after a step power increase, followed by an exponentially decaying recovery after reactor shutdown. A sensitivity analysis based on the governing electro-mechanical equations shows that the frequency shift can be attributed to the softening of sapphire’s elastic constants under neutron radiation. Additionally, a kinetic rate equation is adopted to interpret device response and describe its microstructural evolution. These results suggest that the AlN/sapphire SAW device remains functional under irradiation, is sensitive to neutron and gamma ray fluxes, and offers an opportunity for remote sensing and in-situ measurement of material properties when exposed to nuclear reactor environment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING↗
DOE OSTI2023

New scaling law for turbulent boundary layers with high surface mass transfer

A fundamental understanding of the phenomena occurring in the turbulent boundary layer in the presence of surface blowing is limited, and considerable disagreements persist even in describing primary quantities, such as the boundary layer profile. The theories based on the linear boundary layer equations show that the thickness of the sublayer increases in the presence of surface blowing; therefore, the viscous sublayer and law of the wall modify. In this study, direct numerical simulations (DNS) of turbulent boundary layers with uniform surface mass transfers are carried out in order to scale the velocity profile. Emphasis is placed on moderate to high mass transfer rates, which are relevant to the most common hybrid rockets configuration. DNS data are used to establish a functional law of the wall and a law of wake by means of the relation between the wall shear stress and surface mass transfer. Analysis of the mean kinetic energy budget shows that the magnitude of turbulent kinetic energy increases by surface mass transfer, and the production rate extends significantly in the inner layer as the injection rate increases. DNS data of various surface blowing are used to complete the closure of turbulence kinetic energy equation and develop an eddy viscosity model. The predicted turbulent kinetic energy and eddy viscosity agree with DNS data for moderate to high blowing rates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Hybrid gyrokinetic ion/fluid electron simulation of toroidal tearing modes

The effects of toroidicity and kinetic ions on the resistive tearing mode are systematically studied with the gyrokinetic particle-in-cell simulation code GEM and compared with analytic theory. A new field solver in toroidal geometry has been developed for the simulation of low-n (n = 1, 2) modes in tokamaks. It is found that the toroidal effect significantly reduces the growth rate of the tearing mode. The toroidal effect can also increase the radial width of the tearing mode and change the scaling between the radial mode width and resistivity due to the toroidal pressure term in the electron continuity equation. The kinetic effects of ions can decrease the growth rate of the tearing mode. The plasma flux-surface shaping is found to have significant effect on the tearing mode.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗