SEARCH · Search NASA

Results for “Moment closure”

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.

SourceResearch connectionFrom yearThrough year

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

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Reconstruction of Electron and Ion Distribution Functions in a Magnetotail Reconnection Diffusion Region

In the diffusion region of magnetotail reconnection, particle distributions are highly structured, exhibiting triangular shapes and multiple striations that deviate dramatically from the Maxwellian distribution. Fully kinetic simulations have been demonstrated to be capable of producing the essential structures of the observed distribution functions, yet are computationally not feasible for 3D global simulations. The fluid models used for large-scale simulations, on the other hand, do not have the kinetic physics necessary for describing reconnection accurately. Our study aims to bridge fully kinetic and fluid simulations by quantifying the information required to capture the non-Maxwellian features in the distributions underlying the closures used in the fluid code. Here, we compare the results of fully kinetic simulations with observed electron velocity distributions in a magnetotail reconnection diffusion region and use the maximum entropy model to reconstruct electron and ion distributions using various numbers of moments obtained from the simulation. Our results indicate that using only local moments, the maximum entropy model can reproduce many of the features of the distributions: (1) the electron outflow distribution with a tilted triangular structure is reproduced with 21 or more moments in agreement with Ng et al. and (2) counterstreaming distributions can be captured with the 35-moment model when the separation in velocity space between the populations is large.

58 GEOSCIENCES↗

DOE OSTI2024

Parallel expansion of a fuel pellet plasmoid

The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a ‘quasiequilibrium’ (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation.

Physics↗

DOE OSTI2026

From Weibel seeds to dynamo beyond pair-plasmas

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetised electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropisation and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behaviour qualitatively similar to magnetohydrodynamics.

astrophysical plasmas↗

DOE OSTI2026

Capturing Secondary Kinetic Instabilities in Three‐Dimensional Dayside Reconnection Using an Improved Gradient‐Based Closure

Magnetic reconnection is a highly dynamic process that excites a wide variety of kinetic waves and instabilities. Transverse current sheet instabilities such as the lower-hybrid drift and secondary drift-kink instabilities in particular have been shown by kinetic simulations to modify the reconnection and introduce significant turbulence and mixing to the reconnection layer. Past studies using the ten-moment fluid model to capture important kinetic physics such as the electron inertia and full representation of the pressure tensor proved advantageous to a two-fluid representation of reconnection, but the model struggled when using a local relaxation closure for the heat flux to replicate the current sheet instabilities and subsequent mixing seen in kinetic simulations. This work uses the Gkeyll software framework to perform simulations of asymmetric reconnection based on the 16 October 2015 MMS crossing of a diffusion region, the Burch event. An improved gradient-based heat flux closure is implemented, showing significant improvement in secondary kinetic instabilities that grow in the current sheet. These instabilities generate turbulence which leads to growth of secondary magnetic islands and flux ropes.

Bradshaw, K. [Princeton University, NJ (United Sta↗

DOE OSTI2025

Atwood effects on nonlocality of the scalar transport closure in Rayleigh-Taylor mixing

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (𝐴 = 0.05, 0.3, 0.5, 0.8). It is found that as 𝐴 increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher 𝐴. There is a particularly strong temporal nonlocality at higher 𝐴, suggesting stronger history effects. In conclusion, the implications of these findings for closure modeling for finite-Atwood RT are discussed.

general physics↗

DOE OSTI2024

Advanced Closures for Nonlinear Fluid Simulations of Plasmas (Final Report)

Advanced Closures for Nonlinear Fluid Simulations of Plasmas E. Held, Utah State University (Principal Investigator) J.-Y. Ji, Utah State University (Co-Investigator) Utah State University (USU) continued to develop and apply closures for hybrid fluid/kinetic simulations of magnetized fusion plasmas. The closures developed by USU's fusion theory and computation group use the drift ordering and are referred to as "continuum" and "general moment" approaches. They differ in their representation for the distribution functions which probabilistically describe the density of particles in 5 dimensional phase space. The two chosen velocity variables, needed in studies of kinetic physics for magnetized plasmas, are the speed and the component of a particle's velocity along the magnetic field. In magnetized plasmas, the charged particle trajectories are tied closely to the magnetic field lines. Both approaches account for binary interactions between particles using the Coulomb collision operator. Theoretical and computational development along both lines provided avenues for verification between the two approaches. This funding allowed USU to further develop physically accurate and numerically efficient models that advance our understanding of kinetic physics in experiments like the International Thermonuclear Experimental Reactor (ITER). The ITER device will likely prove the physical practicality of thermonuclear fusion by producing 500 megawatts of clean, abundant fusion power. This work helped to realize this goal by advancing our simulation capability using hybrid fluid/kinetic models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Modeling of the ECCD injection effect on the Heliotron J and LHD plasma stability

The aim of the study is to analyze the stability of the energetic particle modes (EPM) and Alfven Eigenmodes (AE) in Helitron J and LHD plasma if the electron cyclotron current drive (ECCD) is applied. Additionally, the analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. The simulation results show that the n = 1 EPM and n = 2 global AE (GAE) in Heliotron J plasma can be stabilized if the magnetic shear is enhanced at the plasma periphery by an increase (co-ECCD injection) or decrease (ctr-ECCD injection) of the rotational transform at the magnetic axis ($\rlap{-} \iota_{0}$). In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given $\rlap{-} \iota_{0}$, similar to the ECCD intensity threshold observed in the experiments. In addition, ctr-ECCD simulations show an enhancement of the continuum damping. The simulations of the LHD discharges with ctr-ECCD injection indicate the stabilization of the n = 1 EPM, n = 2 toroidal AE (TAE) and n = 3 TAE, caused by an enhancement of the continuum damping in the inner plasma leading to a higher EP β threshold with respect to the co- and no-ECCD simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Emergence of vorticity and viscous stress in finite-scale quantum hydrodynamics

The Madelung equations offer a hydrodynamic description of quantum systems, from single particles to quantum fluids. In this formulation, the probability density is mapped onto the fluid density and the phase is treated as a scalar potential generating the velocity field. As examples of potential flows, quantum fluids described in this way are inherently irrotational, but quantum vortices may arise at discrete points where the phase is undefined. In this paper, starting from this irrotational description of a quantum fluid, a coarse-graining procedure is applied to arrive at a macroscopic description of the quantum fluid in terms of a hierarchy of moments in which the role of velocity is played by a Favre average of the microscopic velocity field. This hierarchy is truncated using an explicit closure derived from an expansion in a finite length scale. The resulting coarse-grained fields are shown to allow for finite vorticity at any point in the fluid. Additionally, it is shown that this vorticity obeys a similar equation to the vorticity equation in classical hydrodynamics and includes a vortex-stretching term. The particular closure employed here also gives rise to a novel stress term in the fluid equations, which in the appropriate limit appears analogous to an artificial viscous stress from computational fluid dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Electron heating in kinetic-Alfvén-wave turbulence

We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). In conclusion, the use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

DOE OSTI2025

HIGH-FIDELITY SIMULATION OF SOOT FORMATION AND THERMAL RADIATION IN A LABORATORY-SCALE RICH-QUENCH-LEAN BURNER

High-fidelity simulations of a swirl-stabilized turbulent spray flame in a laboratory-scale aero-combustor have been performed to evaluate the predictability of state-of-the-art models in capturing soot formation. The simulations employ a complex chemical mechanism developed for Jet-A with PAH chemistry, coupled with the Hybrid Method of Moments (HMOM) soot model, and a Lagrangian dilute spray model for the fuel injection. Two simulations are performed to compare the results when thermal radiation is neglected or included in the solution with a mean spectral model. Modeling closures for the soot differential diffusion effects in mixture fraction space, as well as turbulence-radiation interaction are also evaluated using the data generated by the simulations. Given the degree of complexity of the simulation, the results showed good agreement with experimental measurements of the spatial distribution of the soot volume fraction ensemble average. A closer agreement with the experiment is observed when thermal radiation is included in the solution. Thermal radiation is observed to reduce the flame temperature and increase the flame intermittency, denoted by the increase in the temperature standard deviation in mixture fraction space. The reduction in temperature also leads to a reduction in PAH production and soot volume fraction. Turbulence is observed to have different effects on radiative emission depending on the mixture fraction. Turbulent scalar fluctuations significantly enhance radiative emission in fuel lean mixtures and can also play a role for fuel rich conditions. The statistical description of the turbulence-radiation interaction, previously proposed in the literature, was observed to correctly reproduce the high-fidelity results. Model coefficients were provided for swirl-stabilized flames. The soot differential diffusion model, previously proposed in the literature, based on the residual between the exact term and its model approximation, was also evaluated. The residual correction term further improved the agreement with exact differential diffusion term evaluated with the high-fidelity simulation data in mixture fraction space. The results suggest that the effective turbulent Lewis number can be equal to unity in simulations of turbulent non-premixed recirculating flames.

Soriano, Bruno [Sandia National Laboratories (SNL)↗

DOE OSTI2020

A Plasma Modeling Hierarchy and Verification Approach

This report reviews a hierarchy of formal mathematical models for describing plasma phenomena. Starting with the Boltzmann equation, a sequence of approximations and modeling assumptions can be made that progressively reduce to the equations for magnetohydrodynamics. Understanding the assumptions behind each of these models and their mathematical form is essential to appropriate use of each level of the hierarchy. A sequence of moment models of the Boltzmann equation are presented, then focused into a generalized three-fluid model for neutral species, electrons, and ions. This model is then further reduced to a two-fluid model, for which Braginskii described a useful closure. Further reduction of the two-fluid model yields a Generalized Ohm's Law model, which provides a connection to magnetohydrodynamic approaches. A verification approach based on linear plasma waves is presented alongside the model hierarchy, which is intended as an initial and necessary but not sufficient step for verification of plasma models within this hierarchy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Unified Entrainment and Detrainment Closures for Extended Eddy-Diffusivity Mass-Flux Schemes

The extended Eddy Diffusivity Mass Flux (EDMF) scheme is used as a unied parameterization that simulates subgrid-scale dynamics across a range of regimes.This work presents unied entrainment and detrainment closures that allow this scheme to simulate the dry convective boundary layer, shallow convection and deep convection , while adjacent works present other necessary closures for this unied scheme and test its performance for stable, stratocumulus topped and convective boundary layers. Entrainment and detrainment are modeled as a combination of turbulent and dynamical processes. The turbulent component is taken as downgradient diffusion between subdomains. The dynamical component is based on a ratio of buoyancy and vertical velocity that ensures consistent treatment of the ratio of mass-flux at vanishing area fraction. Dynamical detrainment is controlled by the difference in relative humidity between subdomains when liquid water is present. These closures are rst evaluated with entrainment and detrainment diagnosed from Large Eddy Simulations where decaying tracers are used to identify the different subdomains and mass exchanges between them. When implemented in a single column model (SCM), these closures are tested in simulations of several observationally motivated cases of dry convective boundary layer, shallow convection and deep convection. Results show good agreement between the SCM and Large Eddy Simulations in key properties for climate models and profiles of first, second and third moments. The development of diurnal cycles and the onset of and precipitation (with simplified microphysics) are well predicted by the SCM.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Scale Separation Effects on Simulations of Plasma Turbulence

Abstract Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher-order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfvén speed to the speed of light ( v A / c ) or the relative mass ratio of ions and electrons ( m i / m e ). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the 10-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion–electron mass ratio from a small value down to the realistic proton–electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both plasma species. The dissipative process for both ions and electrons becomes more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous-like heating/dissipation to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio of m i / m e ∼ 250 captures the asymptotic behavior of electron heating.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Fully consistent Eulerian Monte Carlo fields method for solving probability density function transport equations in turbulence modeling

The probability density function (PDF) transport equation method is a sophisticated model for the closure of turbulent mixing and turbulent reactive flows. An efficient solution approach for solving the PDF transport equation has been vital for the method to be widely used in applications. The Eulerian Monte Carlo fields (EMCF) method has been developed to solve the PDF transport equation efficiently for decades. A recent work by Wang et al. revealed a serious issue of the EMCF method for not being fully consistent with the PDF transport equation for which the method is designed to solve. This work advances the state of the art by introducing fully consistent EMCF methods for solving the PDF transport equation. The fully consistent EMCF formulations are derived for two different PDF equation forms. The consistency of the EMCF formulations is mathematically confirmed by examining the derived moment transport equations from the EMCF formulations and from the PDF transport equation. The method of manufactured solutions is employed to further verify the consistency and convergence of the different EMCF formulations numerically. The newly introduced EMCF formulations bring the EMCF method to full consistency with the PDF transport equations for the first time.

42 ENGINEERING↗

DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is γ τ A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of γ τ A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Measurement of the $\textit{B}(\textit{E}2 ↑)$ strengths of 36 Ca and 38 Ca

In this work, the $B(E2, 0^+_1 → 2^+_1)$ strengths of 36 Ca and 38 Ca are measured to be 131(20) $e^2\text{fm}^4$ and 101(11) $e^2\text{fm}^4$, respectively. The $\textit{B}(\textit{E}2)$ value for 36 Ca required a measurement of the p/γ branching ratio because the 2 + state is proton unbound. This branching ratio is $B_p$=0.087(8). These $\textit{B}(\textit{E}2)$ and branching-ratio values can be reproduced in the shell-model with the ZMB2 interaction, an interaction that predicts the $\textit{Z} = 20 \textit{sd}$-shell closure is incomplete with large proton pf-shell occupancies in the ground state. These occupancies are at odds with other shell-model and energy-density-functional calculations of 36 Ca. New data are used to provide an update on constraints of the density dependence of the symmetry energy through mirror charge-radii differences as well as to help reduce uncertainties of the astrophysical important 35 K(p,γ) reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗