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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Diffusive hydrodynamics from integrability breaking

We describe here the crossover from generalized to conventional hydrodynamics in nearly integrable systems. Integrable systems have infinitely many conserved quantities, which spread ballistically, in general. When integrability is broken, only a few of these conserved quantities survive. The remaining conserved quantities are generically transported diffusively; we further derive a compact and general diffusion equation for these. The diffusion constant depends on the matrix elements of the integrability-breaking perturbation; for a certain class of integrability-breaking perturbations, including long-range interactions, the diffusion constant can be expressed entirely in terms of generalized hydrodynamic data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

The propagation of solar flare particles in a turbulent coronal loop

Energetic solar flare particles, both electrons and protons, must survive the turbulent environment of a flaring loop and propogate to the lower corona or chromosphere in order to produce hard X-ray and gamma ray bursts. This plasma turbulence, often observed in soft X-ray line widths to be in excess of 100 km/s, is presumably capable of efficiently scattering the fast flare particles. This prevents to some degree the free streaming of accelerated particles and depending on the amplitude of the turbulence, restricts the particles to diffusive propagation along the length of the loop to the target chromosphere. In addition this turbulence is capable of performing additional acceleration of the fast particles by the second order Fermi mechanism. For compact flares with rise times 10s, the acceleration effect is small and the propagation of the particles is governed by spatial diffusion and energy loss in the ambient medium. The solution of the time dependent diffusion equation with velocity dependent diffusion and energy loss coefficients yields for the case of nonrelativistic protons particle precipitation rates which are necessary for calculating thick target gamma ray emission and also yields the total thin target emissivity.

Ryan, J. M.↗
NASA NTRS1990

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

Jones, Frank C.↗
NASA NTRS1990

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Gutierrez, William E.↗
NASA NTRS1993

CFD analyses of combustor and nozzle flowfields

The objectives of the research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustion processes. A Computational Fluid Dynamic (CFD) technique is employed to model the flowfields within the combustor, nozzle, and near plume field. The computational modeling of the rocket engine flowfields requires the application of the complete Navier-Stokes equations, coupled with species diffusion equations. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an ongoing experimental program at NASA LeRC. The numerical procedure is performed on both time-marching and time-accurate algorithms, using an LU approximate factorization in time, flux split upwinding differencing in space. The integrity of fuel film cooling along the wall, its effectiveness in the mixing with the core flow including unsteady large scale effects, the resultant impact on performance and the assessment of the near plume flow expansion to finite pressure altitude chamber are addressed.

Tsuei, Hsin-Hua↗
NASA NTRS1994

Multi-dimensional combustor flowfield analyses in gas-gas rocket engine

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustions processes. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LeRC. Detailed computational modeling requires the application of the full three-dimensional Navier Stokes equations, coupled with species diffusion equations. The numerical procedure is performed on both time-marching and time-accurate algorithms and using an LU approximate factorization in time, flux split upwinding differencing in space. The emphasis in this paper is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; three-dimensional fuel jets injection/mixing/combustion characteristics; and their impacts on global engine performance.

Tsuei, Hsin-Hua↗
NASA NTRS1994

The Flux-integral Method for Multidimensional Convection and Diffusion

The flux-integral method is a procedure for constructing an explicit, single-step, forward-in-time, conservative, control volume update of the unsteady, multidimensional convection-diffusion equation. The convective plus diffusive flux at each face of a control-volume cell is estimated by integrating the transported variable and its face-normal derivative over the volume swept out by the convecting velocity field. This yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudoflux-difference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation assumed, given cell-average data. Cellwise constant behavior results in a (very artificially diffusive) first-order convection scheme. Second-order convection-diffusion schemes correspond to cellwise linear (or bilinear) subcell interpolation. Cellwise quadratic subcell interpolants generate a highly accurate convection-diffusion scheme with excellent phase accuracy. Under constant-coefficient conditions, this is a uniformly third-order polynomial interpolation algorithm (UTOPIA).

Leonard, B. P.↗
DOE OSTI2023

Required toroidal confinement for fusion and omnigeneity

Deuterium–tritium (DT) burning requires a long energy confinement times compared to collision times, so the particle distribution functions must approximate local Maxwellians. Non-equilibrium thermodynamics is applicable, which gives relations among transport, entropy production, the collision frequency, and the deviation from a Maxwellian. The distribution functions are given by the Fokker–Planck equation, which is an advection–diffusion equation. A large hyperbolic operator, the Vlasov operator with the particle trajectories as its characteristics, equals a small diffusive operator, the collision operator. The collisionless particle trajectories would be chaotic in stellarators without careful optimization. This would lead to rapid entropy production and transport—far beyond what is consistent with a self-sustaining DT burn. Omnigeneity is the weakest general condition that is consistent with a sufficiently small entropy production associated with the thermal particle trajectories. Omnigeneity requires that the contours of constant magnetic field strength be unbounded in at least one of the two angular coordinates in magnetic surfaces and that there be a symmetry in the field-strength wells along the field lines. Even in omnigenous plasmas, fluctuations due to microturbulence can produce chaotic particle trajectories and the gyro-Bohm transport is seen in many stellarator and tokamak experiments. The higher the plasma temperature above 10 keV, the smaller the transport must be compared to gyro-Bohm for a self-sustaining DT burn. The hot alphas of DT fusion heat the electrons. When the ion–electron equilibration time is long compared to the ion energy confinement time, a self-sustaining DT burn is not possible, which sets a limit on the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction–diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: The 2-D case

This is the second part to our companion paper. Herein, we generalize to two space dimensions the C-method developed in for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. Solutions to our C-equations not only indicate the location of the shocks and contacts, but also track the geometry of the evolving fronts. This allows us to implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska & Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-oscillatory solution, even though our simplified WENO-type scheme fails to run for this problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Stochastic acceleration of energetic ions in Jupiter's magnetosphere

An equation governing the combined radial diffusion and stochastic acceleration of super-Alfvenic ions by magnetohydrodynamic waves in Jupiter's outer magnetosphere is derived. The formulation is based upon a total energy invariant of the adiabatic transport which applies to an isotropic distribution undergoing rapid pitch angle scattering by waves. An analytic solution to the double diffusion equation is obtained and numerical results are presented for two models of ion injection. The first model assumes S(+) and O(+) are injected throughout a broad region of space through photoionization of Jupiter's magnetospheric neutral wind and obtain an initial energy corresponding to the local corotation energy after pickup by the planetary magnetic field. The second model assumes a monoenergetic distribution of energetic protons is implanted in the middle magnetosphere by the action of field-aligned potential drops in Jupiter's auroral ionosphere. For both light and heavy ions the injection process creates a seed population of particles which are further accelerated nonadiabatically by the MHD waves and adiabatically through radial diffusion. A comparison of the theoretical results with a recent data analysis of Voyager low-energy charged particle measurements is made with very good agreement, thus providing a rigorous quantitative account of and definitive explanation for the high-energy ion component of Jupiter's magnetosphere.

Barbosa, D. D.↗
DOE OSTI2019

Determination of the Thicknesses and Visualization of Ion-Exchange Waveguides in Glasses by Scanning Electron Microscopy

The formation of a surface layer with silver and sodium concentration gradients in K8-grade glasses as a result of ion exchange is demonstrated by scanning electron microscopy (SEM) and electron probe X-ray microanalysis. The silver ions enriched layers with different thicknesses, depending on the duration of the ion exchange from the silver melt, are visualized in the secondary electrons mode. SEM data on the thickness of the silver enriched layer are in good agreement with the results of calculation from the diffusion equation for silver in glass. The dependence of the silver concentration on the diffusion depth is obtained using elemental composition mapping over the glass cross section. The presence of a layer with a silver concentration gradient leads to formation of a gradient waveguide. Discrete peaks in silver concentration profiles, caused by specific features of mutual diffusion of sodium and silver ions in glasses, are found.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Resistive drift wave turbulence and anomalous transport of multi-species plasma

Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.

Physics↗
DOE OSTI2018

Lessons from HAWC pulsar wind nebulae observations: The diffusion constant is not a constant; pulsars remain the likeliest sources of the anomalous positron fraction; cosmic rays are trapped for long periods of time in pockets of inefficient diffusion

Recent TeV observations of nearby pulsars with the HAWC telescope have been interpreted as evidence that the diffusion of high-energy electrons and positrons within pulsar wind nebulae is highly inefficient compared to the rest of the interstellar medium. If the diffusion coefficient well outside the nebula is close to the value inferred for the region inside the nebula, high-energy electrons and positrons produced by the two observed pulsars could not contribute significantly to the local measured cosmic-ray flux. The HAWC Collaboration thus concluded that, under the assumption of isotropic and homogeneous diffusion, the two pulsars are ruled out as sources of the anomalous high-energy positron flux. Here, we argue that since the diffusion coefficient is likely not spatially homogeneous, the assumption leading to this conclusion is flawed. We solve the diffusion equation with a radially dependent diffusion coefficient, and show that the pulsars observed by HAWC produce potentially perfect matches to the observed high-energy positron fluxes. We also study the implications of inefficient diffusion within pulsar wind nebulae on Galactic scales, and show that cosmic rays are likely to have very long residence times in regions of inefficient diffusion. We describe how this prediction can be tested with studies of the diffuse Galactic emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Final Report - Subcontract B629114

During my visits to LLNL August 20-24, 2018, and September 10-14, 2018, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from $hp$ adaptive finite element calculations, and is implemented in the PLTMG software package, version 13. This preconditioner typically requires 3 – 20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree $p$ as $p → ∞$, but but remains strong for $p ≤$ 9, which is the highest polynomial degree allowed in PLTMG , due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Subcontract B635525 (Final Report)

During my visits to LLNL July 8–12 and July 22–26, 2019, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from $\textit{hp}$ adaptive finite element calculations, and is implemented in the $\textit{PLTMG}$ software package, version 13. This preconditioner typically requires 3–20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree $\textit{p}$ as $\textit{p} → ∞$, but remains strong for $\textit{p}$ ≤ 9, which is the highest polynomial degree allowed in $\textit{PLTMG}$, due to limitations of the numerical quadrature rules implemented in the soft- ware package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.

97 MATHEMATICS AND COMPUTING↗