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NASA NTRS2002

Challenging Cosmic Ray Propagation with Antiprotons: Evidence for a "Fresh" Nuclei Component?

Recent measurements of the cosmic ray (CR) antiproton flux have been shown to challenge existing CR propagation models. It was shown that the reacceleration models designed to match secondary to primary nuclei ratio (e.g., Boron/Carbon) produce too few antiprotons, while the traditional non-reacceleration models can reproduce the antiproton flux but fall short of explaining the low-energy decrease in the secondary to primary nuclei ratio. Matching both the secondary to primary nuclei ratio and antiproton flux requires artificial breaks in the diffusion coefficient and the primary injection spectrum suggesting the need for other approaches. In the present paper we discuss one possibility to overcome these difficulties. Using the measured antiproton flux to fix the diffusion coefficient, we show that the spectra of primary nuclei as measured in the heliosphere may contain a fresh local unprocessed component at low energies, thus decreasing the measured secondary to primary nuclei ratio. A model reproducing antiprotons, B/C ratio, and abundances up to Ni is presented.

Moskalenko, Igor V.↗

NASA NTRS1998

Comments on the Diffusive Behavior of Two Upwind Schemes

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Wood, William A.↗

NASA NTRS1998

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Wood, William A.↗

NASA NTRS1992

ULTRA-SHARP solution of the Smith-Hutton problem

Highly convective scalar transport involving near-discontinuities and strong streamline curvature was addressed in a paper by Smith and Hutton in 1982, comparing several different convection schemes applied to a specially devised test problem. First order methods showed significant artificial diffusion, whereas higher order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low order artificially diffusive schemes, especially in the numerical heat transfer industry. The present paper describes an alternate strategy of using non-artificially diffusive high order methods, while maintaining strictly monotonic transitions through the use of simple flux limited constraints. Limited third order upwinding is usually found to be the most cost effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Leonard, B. P.↗

NASA NTRS2010

Diffuse-Illumination Systems for Growing Plants

Agriculture in both terrestrial and space-controlled environments relies heavily on artificial illumination for efficient photosynthesis. Plant-growth illumination systems require high photon flux in the spectral range corresponding with plant photosynthetic active radiation (PAR) (400 700 nm), high spatial uniformity to promote uniform growth, and high energy efficiency to minimize electricity usage. The proposed plant-growth system takes advantage of the highly diffuse reflective surfaces on the interior of a sphere, hemisphere, or other nearly enclosed structure that is coated with highly reflective materials. This type of surface and structure uniformly mixes discrete light sources to produce highly uniform illumination. Multiple reflections from within the domelike structures are exploited to obtain diffuse illumination, which promotes the efficient reuse of photons that have not yet been absorbed by plants. The highly reflective surfaces encourage only the plant tissue (placed inside the sphere or enclosure) to absorb the light. Discrete light sources, such as light emitting diodes (LEDs), are typically used because of their high efficiency, wavelength selection, and electronically dimmable properties. The light sources are arranged to minimize shadowing and to improve uniformity. Different wavelengths of LEDs (typically blue, green, and red) are used for photosynthesis. Wavelengths outside the PAR range can be added for plant diagnostics or for growth regulation

May, George↗

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.↗

NASA NTRS2013

Uncertainty Determination for Aeroheating in Uranus and Saturn Probe Entries by the Monte Carlo Method

The 2013-2022 Decaedal survey for planetary exploration has identified probe missions to Uranus and Saturn as high priorities. This work endeavors to examine the uncertainty for determining aeroheating in such entry environments. Representative entry trajectories are constructed using the TRAJ software. Flowfields at selected points on the trajectories are then computed using the Data Parallel Line Relaxation (DPLR) Computational Fluid Dynamics Code. A Monte Carlo study is performed on the DPLR input parameters to determine the uncertainty in the predicted aeroheating, and correlation coefficients are examined to identify which input parameters show the most influence on the uncertainty. A review of the present best practices for input parameters (e.g. transport coefficient and vibrational relaxation time) is also conducted. It is found that the 2(sigma) - uncertainty for heating on Uranus entry is no more than 2.1%, assuming an equilibrium catalytic wall, with the uncertainty being determined primarily by diffusion and H(sub 2) recombination rate within the boundary layer. However, if the wall is assumed to be partially or non-catalytic, this uncertainty may increase to as large as 18%. The catalytic wall model can contribute over 3x change in heat flux and a 20% variation in film coefficient. Therefore, coupled material response/fluid dynamic models are recommended for this problem. It was also found that much of this variability is artificially suppressed when a constant Schmidt number approach is implemented. Because the boundary layer is reacting, it is necessary to employ self-consistent effective binary diffusion to obtain a correct thermal transport solution. For Saturn entries, the 2(sigma) - uncertainty for convective heating was less than 3.7%. The major uncertainty driver was dependent on shock temperature/velocity, changing from boundary layer thermal conductivity to diffusivity and then to shock layer ionization rate as velocity increases. While radiative heating for Uranus entry was negligible, the nominal solution for Saturn computed up to 20% radiative heating at the highest velocity examined. The radiative heating followed a non-normal distribution, with up to a 3x variation in magnitude. This uncertainty is driven by the H(sub 2) dissociation rate, as H(sub 2) that persists in the hot non-equilibrium zone contributes significantly to radiation.

Palmer, Grant↗

NASA NTRS1994

Analysis and design of numerical schemes for gas dynamics. 2: Artificial diffusion and discrete shock structure

The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristics splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP scheme in which the coefficients of the pressure differences is fully determined by the coefficient of convective diffusion. It is also shown how both the characteristic and CUSP schemes can be modified to preserve constant stagnation enthalpy in steady flow, leading to four variants, the E and H-characteristic schemes, and the E and H-CUSP schemes. Numerical results are presented which confirm the properties of these schemes.

Jameson, Antony↗

NASA NTRS1999

Diffusion, Fluxes, Friction Forces, and Joule Heating in Two-Temperature Multicomponent Magnetohydrodynamics

The relationship between Joule heating, diffusion fluxes, and friction forces has been studied for both total and electron thermal energy equations, using general expressions for multicomponent diffusion in two-temperature plasmas with the velocity dependent Lorentz force acting on charged species in a magnetic field. It is shown that the derivation of Joule heating terms requires both diffusion fluxes and friction between species which represents the resistance experienced by the species moving at different relative velocities. It is also shown that the familiar Joule heating term in the electron thermal energy equation includes artificial effects produced by switching the convective velocity from the species velocity to the mass-weighted velocity, and thus should not be ignored even when there is no net energy dissipation.

Chang, C. H.↗

NASA NTRS1992

Numerical simulations using a dynamic solution-adaptive grid algorithm, with applications to unsteady internal flows

An investigation into the numerical simulation of unsteady flows is undertaken using a two-stage Runge-Kutta scheme coupled with the dynamic solution-adaptive grid algorithm developed by the authors. The inviscid fluxes are described by a modified Advective Upwind Split Method to eliminate the need for artificial dissipation. A well-documented numerical example containing moving discontinuities is presented that demonstrates the ability of the coupled grid/solver scheme to accurately capture unsteady flowfield phenomena. Applications are to a typical inlet diffuser configuration at Mach 3.0 with excessive back pressure inducing inlet unstart.

Benson, Rusty A.↗

NASA NTRS2011

Radiation Belt Environment Model: Application to Space Weather and Beyond

Understanding the dynamics and variability of the radiation belts are of great scientific and space weather significance. A physics-based Radiation Belt Environment (RBE) model has been developed to simulate and predict the radiation particle intensities. The RBE model considers the influences from the solar wind, ring current and plasmasphere. It takes into account the particle drift in realistic, time-varying magnetic and electric field, and includes diffusive effects of wave-particle interactions with various wave modes in the magnetosphere. The RBE model has been used to perform event studies and real-time prediction of energetic electron fluxes. In this talk, we will describe the RBE model equation, inputs and capabilities. Recent advancement in space weather application and artificial radiation belt study will be discussed as well.

Fok, Mei-Ching H.↗

NASA NTRS2000

Formation of Leading-Edge Pinholes in the Space Shuttle Wings Investigated

The space shuttle wing leading edge and nose cap are composed of a carbon/carbon composite that is protected by silicon carbide. The coefficient of thermal expansion mismatch leads to cracks in the silicon carbide. The outer coating of the silicon carbide is a sodium-silicate-based glass that becomes fluid at the shuttles high reentry temperatures and fills these cracks. Small pinholes roughly 0.1 mm in diameter have been observed on these materials after 12 or more flights. These pinholes have been investigated by researchers at the NASA Johnson Space Center, Rockwell International, the Boeing Company, Lockheed Martin Corporation, and the NASA Glenn Research Center at Lewis Field to determine the possible sources and the extent of damage. A typical pinhole is illustrated in the photomicrographs. These pinholes are found primarily on the wing leading edges and not on the nose cap, which is covered when the orbiter is on the launch pad. The pinholes are generally associated with a bead of zincrich glass. Examination of the orbiter and launch structure indicates that weathering paint on the launch structure leads to deposits of zinc-containing paint flakes on the wing leading edge. These may become embedded in the crevices of the wing leading edge and form the observed zinc-rich glass. Laboratory experiments indicate that zinc oxide reacts vigorously with the glass coating on the silicon carbide. Thus, it is likely that this is the reaction that leads to pinhole formation (Christensen, S.V.: Reinforced Carbon/Carbon Pin Hole Formation Through Zinc Oxide Attack. Rockwell International Internal Letter, RDW 96 057, May 1996). Cross-sectional examination of pinholes suggests that they are enlarged thermal expansion mismatch cracks. This is illustrated in the photomicrographs. A careful microstructural analysis indicates that the pinhole walls consist of layers of zinc-containing glass. Thus, pinholes are likely formed by zinc oxide particles lodging in crevices and forming a corrosive zinc-rich glass that enlarges existing cracks. Having established the likely source of the pinholes, we next needed to model the damage. Our concern was that if a pinhole went through the silicon carbide to the carbon/carbon substrate, oxygen would have a clear path to oxidize the carbon at high temperatures. This possibility was examined with studies in a laboratory furnace. An ultrasonic drill was used to make artificial pinholes in a sample of protected carbon/carbon. After exposure, the specimens were weighed and cross-sectioned to quantify the extent of oxidation below the pinhole. The results at higher temperatures showed good agreement with a simple diffusion-control model. This model is based on the two-step oxidation of carbon to carbon monoxide and carbon dioxide. The fluxes are illustrated in the final figure. The model indicates a strong dependence on pinhole diameter. For smaller diameters and short times, the oxidation of carbon is very limited.

Jacobson, Nathan S.↗

NASA NTRS2004

Water cycle and its management for plant habitats at reduced pressures

Experimental and mathematical models were developed for describing and testing temperature and humidity parameters for plant production in bioregenerative life support systems. A factor was included for analyzing systems operating at low (10-101.3 kPa) pressure to reduce gas leakage and structural mass (e.g., inflatable greenhouses for space application). The expected close relationship between temperature and relative humidity was observed, along with the importance of heat exchanger coil temperature and air circulation rate. The presence of plants in closed habitats results in increased water flux through the system. Changes in pressure affect gas diffusion rates and surface boundary layers, and change convective transfer capabilities and water evaporation rates. A consistent observation from studies with plants at reduced pressures is increased evapotranspiration rates, even at constant vapor pressure deficits. This suggests that plant water status is a critical factor for managing low-pressure production systems. The approach suggested should help space mission planners design artificial environments in closed habitats.

NASA Center KSC↗

NASA NTRS1990

ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

Leonard, B. P.↗

NASA NTRS1994

Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

Jameson, Antony↗

NASA NTRS2001

Reverse osmosis filtration for space mission wastewater: membrane properties and operating conditions

Reverse osmosis (RO) is a compact process that has potential for the removal of ionic and organic pollutants for recycling space mission wastewater. Seven candidate RO membranes were compared using a batch stirred cell to determine the membrane flux and the solute rejection for synthetic space mission wastewaters. Even though the urea molecule is larger than ions such as Na+, Cl-, and NH4+, the rejection of urea is lower. This indicates that the chemical interaction between solutes and the membrane is more important than the size exclusion effect. Low pressure reverse osmosis (LPRO) membranes appear to be most desirable because of their high permeate flux and rejection. Solute rejection is dependent on the shear rate, indicating the importance of concentration polarization. A simple transport model based on the solution-diffusion model incorporating concentration polarization is used to interpret the experimental results and predict rejection over a range of operating conditions. Grant numbers: NAG 9-1053.

Non-NASA Center↗

NASA NTRS1983

A study of plasmaspheric density distributions for diffusive equilibrium conditions

The plasmaspheric density distribution has been modeled for a range of solar cycle, seasonal and diurnal conditions with a magnetic flux tube dependent diffusive equilibrium model by using experimentally determined values of ionospheric parameters at 675 km as boundary conditions. Data is presented in terms of plasmaspheric H(+) and He(+) density contours, total flux tube content, and equatorial plasma density for a range of L-values from 1.15 to 3.0. The variation of equatorial density with L-value shows good agreement with the 1/L exp 4 dependence observed experimentally. The results show that the model predicts larger solar cycle and diurnal variation in equatorial plasma density than observed using whistler techniques. However, the whistler method requires a model to deduce the equatorial density and is therefore open to interpretation. Seasonal variations are rather artificial since in this general model no attempt has been made to match equatorial densities for flux tubes emanating from the winter and summer hemispheres.

Li, W.↗

NASA NTRS1997

The Implicit and Explicit alpha-mu Schemes

Artificial numerical dissipation is an important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The method of space-time conservation element and solution element, currently under development, is a nontraditional numerical method for solving conservation laws. The method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. Explicit solvers for model and fluid dynamic conservation laws have previously been investigated. In this paper, we introduce a new concept in the design of implicit schemes, and use it to construct two highly accurate solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to purely inviscid (convective) equations. The stability and consistency of the schemes are analyzed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme. We also construct an explicit solver with the treatment of diffusion being based on that in the implicit solvers. The explicit solver has only a CFL stability limitation on the Courant number, yet it retains the second-order spatial accuracy of the implicit schemes.

Chang, Sin-Chung↗