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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Phase-Field Model for In-Space Manufacturing of Binary Alloys

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Physics↗
DOE OSTI2025

Dynamics of heavy quarks in strongly coupled $\mathcal{N}$ = 4 SYM plasma

We calculate the probability distribution P(k) for a heavy quark with velocity v propagating through strongly coupled N = 4 SYM plasma in the ’t Hooft limit (N c → ∞, λ = g 2 N c → ∞) at a temperature T to acquire a momentum k due to interactions with the plasma. This distribution encodes the well-known drag coefficient η D and the transverse and longitudinal momentum diffusion coefficients κ T and κ L . The jet quenching parameter $\hat{q}$ can be extracted from P(k) for v = 1. Going beyond these known Gaussian characteristics of P(k), our calculation determines all of the higher order and mixed moments to leading order in 1/$\sqrt{λ}$ for the first time. These non-Gaussian features of P(k) include qualitatively novel correlations between longitudinal energy loss and transverse momentum broadening at nonzero v. We show that all higher moments scale characteristically with an effective temperature of the boosted plasma in the heavy quark rest frame, and we demonstrate that these non-Gaussian characteristics can be sizable in magnitude and even dominant in physically relevant situations. We use these results to derive a Kolmogorov equation for the evolution of the probability distribution for the total momentum of a heavy quark that propagates through strongly coupled plasma. This evolution equation accounts for all higher order correlations between transverse momentum broadening and longitudinal energy loss, which we have calculated from first principles. It reduces to a Fokker-Planck equation when truncated to only include the effects of η D , κ T and κ L . Remarkably, while heavy quarks do not reach kinetic equilibrium with the plasma if evolved with this Fokker-Planck equation, by showing that the Boltzmann distribution is a static solution of the all-order Kolmogorov equation that we have derived we demonstrate that heavy quarks do reach kinetic equilibrium if evolved with this equation. Our results thus provide a dynamically complete framework for understanding the thermalization of a heavy quark that may be initially far from equilibrium in the strongly coupled N = 4 SYM plasma — as well as new insight into heavy quark transport and equilibration in quark-gluon plasma.

Holography and Hydrodynamics↗
DOE OSTI2024

Vapor kinetic energy for the detection and understanding of atmospheric rivers

Poleward water vapor transport in the midlatitudes mainly occurs in meandering filaments of intense water vapor transport, spanning thousands of kilometers long and hundreds of kilometers wide and moving eastward. The water vapor filaments are known as atmospheric rivers (ARs). They can cause extreme wind gusts, intense precipitation, and flooding along densely populated coastal regions. Many recent studies about ARs focused on the statistical analyses of ARs, but a process-level understanding of ARs remains elusive. Here we show that ARs are streams of air with enhanced vapor kinetic energy (VKE) and derive a governing equation for Integrated VKE to understand what contributes to the evolution of ARs. We find that ARs grow mainly because of potential energy conversion to kinetic energy, decay largely owing to condensation and turbulence, and the eastward movement is primarily due to horizontal advection of VKE. Our VKE framework complements the integrated vapor transport framework, which is popular for identifying ARs but lacks a prognostic equation for understanding the physical processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Spiers Memorial Lecture: Theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our ability to model and predict the kinetics of such reactions has grown in leaps and bounds through the synergy of ever more sophisticated experimental studies with increasingly high level theoretical analyses. Herein, this review begins with a brief historical overview of the progress from the Lindemann mechanism to the master equation, which now provides the cornerstone for most theoretical analyses. The current status of ab initio transition state theory based implementations of the master equation is then reviewed, beginning with a discussion of the energy resolved chemical conversion rates, followed by a review of the pressure dependence of the thermal kinetics. The latter discussion focusses on the collisional energy and angular momentum transfer rates as well as the complexities of non-thermal effects and of multiple-well multiple-channel reactions. The synergy with recent state-of-the-art experiments is used to motivate these discussions. Attempts to automate the calculations are also briefly reviewed. Throughout the discussion, we provide our perspective on current understanding and continuing challenges and opportunities. One key challenge relates to the coupling of sequences of reactions, which frequently leads to deviations from the classic presumption of thermal reactants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A consistent and conservative Phase-Field method for multiphase incompressible flows

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space

Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold. Casimir invariants are special invariants that depend on the Poisson bracket, not on the particular choice of the Hamiltonian. The total mass (or particle number) is another Casimir invariant, whose invariance guarantees the mass (particle) conservation (independent of any specific choice of the Hamiltonian). In a kinetic description (e.g., that of the Vlasov equation), the helicity is no longer an invariant (although the total mass remains a Casimir of the Vlasov’s Poisson algebra). The implication is that some “kinetic effect” can violate the constancy of the helicity. To elucidate how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid (macroscopic) system is a “sub-algebra” of the kinetic (microscopic) Vlasov system. In the Vlasov system, the helicity can be conserved if a special helicity symmetry condition holds. To put it another way, breaking helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of helicity symmetry and show that for a special class of flows (the so-called epi-two-dimensional flows), the helicity symmetry is written as ∂γ = 0 for a coordinate γ of the configuration space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Machine learning of hidden variables in multiscale fluid simulation

Solving fluid dynamics equations often requires the use of closure relations that account for missing microphysics. For example, when solving equations related to fluid dynamics for systems with a large Reynolds number, sub-grid effects become important and a turbulence closure is required, and in systems with a large Knudsen number, kinetic effects become important and a kinetic closure is required. By adding an equation governing the growth and transport of the quantity requiring the closure relation, it becomes possible to capture microphysics through the introduction of ‘hidden variables’ that are non-local in space and time. The behavior of the ‘hidden variables’ in response to the fluid conditions can be learned from a higher fidelity or ab-initio model that contains all the microphysics. In our study, a partial differential equation simulator that is end-to-end differentiable is used to train judiciously placed neural networks against ground-truth simulations. We show that this method enables an Euler equation based approach to reproduce non-linear, large Knudsen number plasma physics that can otherwise only be modeled using Boltzmann-like equation simulators such as Vlasov or particle-in-cell modeling.

42 ENGINEERING↗
DOE OSTI2026

Characterizing Turbulence at a Forest Edge: Comparing Sub-Filter Scale Turbulence Models in Simulations of Flow over a Canopy

In wildfires, atmospheric turbulence plays a major role in the transfer of turbulent kinetic energy. Understanding how turbulence feeds back into a dynamical system is important, down to the varying small scales of fuel structures (i.e. pine needles, grass). Large eddy simulations (LES) are a common way of numerically representing turbulence. The Smagorinsky model (1963) serves as one of the most studied sub-grid scale representations in LES. In this investigation, the Smagorinsky model was implemented in HIGRAD/FIRETEC, LANL’s coupled fire-atmosphere model. This study was motivated by the need to quantitatively investigate the vorticity budget equation in HIGRAD/FIRETEC. The Smagorinsky turbulent kinetic energy (TKE) was compared to FIRETEC’s 1.5-order TKE eddy-viscosity subgrid-scale model, known as the Linn turbulence model. This was done in simulations of flow over flat terrain with a homogeneous, cuboidal canopy in the center of the domain. Examinations of the modeled vertical TKE profile and turbulent statistics at the leading edge, and throughout the canopy, show that the Smagorinsky model provides comparable results to that of the original closure model posed in FIRETEC.

58 GEOSCIENCES↗
DOE OSTI2021

Code Development Supporting a Non-Thermal Source of High Fluence Warm X-Ray

A six-month research effort has advanced the hybrid kinetic-fluid modeling capability required for developing non-thermal warm x-ray sources on Z. The three particle treatments of quasi-neutral, multi-fluid, and kinetic are demonstrated in 1D simulations of an Ar gas puff. The simulations determine required resolutions for the advanced implicit solution techniques and debug hybrid particle treatments with equation-of-state and radiation transport. The kinetic treatment is used in preliminary analysis of the non-Maxwellian nature of a gas target. It is also demonstrates the sensitivity of the cyclotron and collision frequencies in determining the transition from thermal to non-thermal particle populations. Finally, a 2D Ar gas puff simulation of a Z shot demonstrates the readiness to proceed with realistic target configurations. The results put us on a very firm footing to proceed to a full LDRD which includes continued development transition criteria and x-ray yield calculation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Competing Radical and Molecular Channels in the Unimolecular Dissociation of Methylformate

The thermal dissociation of methylformate has been characterized by numerous experimental and theoretical studies that all seem to agree that the lowest energetically accessible process is a 3-center H-atom transfer that leads to the molecular products CH3OH 3 OH + CO. However, these literature studies seem to be at odds with regards to the role of other competing molecular eliminations and bond-fission processes and therefore a complete and resolved mechanistic picture of methylformate thermal dissociation still eludes us. In this work, we have performed high-level electronic structure theory calculations to characterize the energetics of other overlooked molecular and radical processes that can originate on the complex CH3OCHO 3 OCHO potential energy surface (PES). The present calculations do indeed confirm that the lowest energy process accessible on this PES is molecular elimination to form CH3OH 3 OH + CO. However, unlike prior theoretical studies, the present calculations reveal that the second lowest energy process is a 5-center concerted elimination process that leads to the direct formation of H2 2 + CH2O 2 O + CO. We also note that HCO2 2 from the lowest-lying bond fission has two energetically comparable electronic states (of 2 B 2 and 2 A 1 symmetry). Furthermore, the barrier for H-atom migration of CH3OCHO 3 OCHO to form the carbene (CH3OCOH) 3 OCOH) is similar to that for the direct 4-center elimination process leading to CH2O 2 O + CH2O 2 O characterized in prior literature studies. Radical and molecular pathways to CH3 3 + HOCO and CH4 4 + CO2 2 can also be facilitated from this carbene. Master equation calculations were performed to characterize the competition between the various molecular and radical processes on this more elaborate CH3OCHO 3 OCHO PES. The results of the present theoretical analyses were used to resolve outstanding questions on the role of secondary radical- initiated reactions in characterizing prior literature experimental studies.

Chemical Kinetics↗
DOE OSTI2023

Optimizing the electron transport chain to sustainably improve photosynthesis

Abstract Genetically improving photosynthesis is a key strategy to boosting crop production to meet the rising demand for food and fuel by a rapidly growing global population in a warming climate. Many components of the photosynthetic apparatus have been targeted for genetic modification for improving photosynthesis. Successful translation of these modifications into increased plant productivity in fluctuating environments will depend on whether the electron transport chain (ETC) can support the increased electron transport rate without risking overreduction and photodamage. At present atmospheric conditions, the ETC appears suboptimal and will likely need to be modified to support proposed photosynthetic improvements and to maintain energy balance. Here, I derive photochemical equations to quantify the transport capacity and the corresponding reduction level based on the kinetics of redox reactions along the ETC. Using these theoretical equations and measurements from diverse C3/C4 species across environments, I identify several strategies that can simultaneously increase the transport capacity and decrease the reduction level of the ETC. These strategies include increasing the abundances of reaction centers, cytochrome b6f complexes, and mobile electron carriers, improving their redox kinetics, and decreasing the fraction of secondary quinone–nonreducing photosystem II reaction centers. I also shed light on several previously unexplained experimental findings regarding the physiological impacts of the abundances of the cytochrome b6f complex and plastoquinone. The model developed, and the insights generated from it facilitate the development of sustainable photosynthetic systems for greater crop yields.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Dispersion relation for gauge-free electromagnetic drift kinetics

Recently, a new approach to gyrokinetics, invariant under electromagnetic gauge transformations, was developed. The gyrocenter equations of motion are now expressed in terms of the perturbed fields instead of the potentials, in a form suitable for numerical simulations and analytic studies. In this paper, we verify that the long-wavelength limit, i.e., the drift-kinetic limit of the new gyrokinetic theory, is in line with existing work, providing a solid foundation for simulations. Here, we compute the dispersion relation of the new drift-kinetic theory in slab geometry and find agreement with a long-wavelength limit of the full Vlasov–Maxwell model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Verification of a specialized hydrodynamic simulation code for modeling deflagration and detonation of high explosives

A specialized hydrodynamic simulation code has been developed and verified for the simulation of one-dimensional unsteady problems involving the detonation and deflagration of high explosives. To model all the relevant physical processes in these problems, a code is required to simulate compressible hydrodynamics, unsteady thermal conduction, and chemical reactions with complex rate laws. Several verification exercises are presented which test the implementation of these capabilities. The code also requires models for physics processes such as equations of state and conductivity for pure materials and mixtures as well as rate laws for chemical reactions. Additional verification tests are required to ensure that these models are implemented correctly. Though this code is limited in the types of problems it can simulate, its computationally efficient formulation allows it to be used in calibration studies for reactive burn models for high explosives. Furthermore, this study demonstrates how a series of verification tests can be used to ensure that the various physics processes needed to simulate complex phenomenon can be tested to ensure that they are correctly implemented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Anomalous conductivity due to relativistic Landau quantization

Here we use a recently developed kinetic model derived from the Dirac equation, in order to study electromagnetic wave propagation in superstrong magnetic fields, such as in magnetars, where relativistic Landau quantization is prominent. The leading contribution to the conductivity tensor in such a plasma is calculated. It is found that the electron Hall current has an anomalous contribution, in the quantum relativistic regime, where the effective particle energy has a significant contribution from the diamagnetic and Zeeman energy. As a result, a new quantum resonance frequency appears, and the dispersion relation for the left- and right-hand polarized modes are strongly modified for long and moderate wavelengths. The implications for magnetar physics are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

The role of collisional energy transfer in the thermal and prompt dissociation of 1-methyl allyl

Collisional energy transfer plays a pivotal role in a-priori calculations of the pressure-dependent rate constants obtained from a master equation. However, accurate determinations of collisional energy transfer parameters are rare and so most kinetic studies rely on best-fits of these parameters to experimental measurements (if available) or estimates guided from literature studies. In this work, we have quantified the effect of the uncertainty in energy transfer parameters on the thermal and prompt dissociation kinetics of a resonance stabilized radical, 1-methyl allyl (1MA), of relevance to the combustion of 1- and 2-butene isomers. Simulations using literature kinetics models were performed to assess the impact of these uncertainties on flame propagation and speciation data in laminar flames of 1- and 2-butene. Analyses of the uncertainty propagated by the energy transfer parameters for 1MA dissociation to the flame simulations, in particular the laminar flame speed, indicate an intricate coupling between the kinetics of 1MA dissociation (chain propagation) and its reaction with H-atoms (chain-termination). Ab-initio based theoretical calculations were also performed to obtain pressure-dependent kinetics for the reaction of 1MA with H-atoms. Lastly, theoretically calculated energy transfer parameters were used to best characterize the kinetics and branching between the chain propagating 1MA dissociation and the chain-terminating reaction 1MA + H.

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

Asymptotic Relaxation of Moment Equations for a Multi-species, Homogeneous BGK Model

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially nontrivial velocity distributions. Here, in this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large times.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

HȮ 2 + HȮ 2 : High level theory and the role of singlet channels

At low temperatures and high pressures, the HȮ 2 + HȮ 2 reaction is an important reaction in combustion. There are significant unresolved discrepancies between prior theoretical and experimental studies of this reaction. It has generally been presumed to occur as an abstraction on the triplet surface to produce H 2 O 2 + 3 O 2 . Here, we employ a combination of high-level electronic structure theory (the ANL0 composite method or multi-reference methods as appropriate), sophisticated transition state theory (vibrationally adiabatic torsions, variational, and variable reaction coordinate), and master equation analyses to predict the thermal kinetics on the H 2 O 4 surface. Notably, this analysis suggests a significant branching to HȮ 3 + ȮH near 1000 K via reaction on the singlet surface. This channel does not appear to have been considered in prior combustion models. HȮ 3 itself is a metastable complex (bound by only 3 kcal mol -1 ) that rapidly dissociates to ȮH + 3 O 2 . Thus, the net reaction for this channel, HȮ 2 + HȮ 2 → ȮH + ȮH + O 2 , converts two low reactivity HȮ 2 radicals into two highly reactive ȮH radicals. The ramifications of these newly derived rate expressions are highlighted through kinetic modeling studies of H 2 , CH 3 OH, $\textit{n}$-heptane, and isooctane oxidation; all at the high pressures of relevance to combustion devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗