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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Multigrid methods for numerical simulation of laminar diffusion flames

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

Liu, C.↗
NASA NTRS1978

Numerical analyses for treating diffusion in single-, two- and three-phase binary alloy systems

Numerical solutions were applicable for planar, cylindrical, or spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included in the analyses to account for differences in molal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. A major improvement in solution accuracy was achieved in the two phase analysis by employing a mass conservation criterion to establish the location of the interface rather than the conventional interface-flux-balance criterion. In the three phase analysis, computation time was minimized without sacrificing solution accuracy by treating the three phase problem as a two phase problem when the thickness of the intermediate phase was less than a preset small value. Three computer codes were developed to perform these analyses.

Tenney, D. R.↗
NASA NTRS2011

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Cacio, Emanuela↗
NASA NTRS1998

3-D Modeling of Directional Solidification of a Non-Dilute Alloy with Temperature and Concentration Fields Coupling via Materials Properties Dependence and via Double Diffusive Convection

Numerical simulation of the HgCdTe growth by the vertical Bridgman method was performed using FIDAP finite element code. Double-diffusive melt convection is analyzed, as the primary factor at controls inhomogeneity of the solidified material. Temperature and concentration fields in the model are also coupled via material properties, such as thermal and solutal expansion coefficients with the dependence on both temperature and concentration, and melting temperature evaluation from pseudobinary CdTe-HgTe phase diagram. Experimental measurements were used to obtain temperature boundary conditions. Parametric study of the melt convection dependence on the gravity conditions was undertaken. It was found, that the maximum convection velocity in the melt can be reduced under certain conditions. Optimal conditions to obtain a near flat solidified interface are discussed. The predicted interface shape is in agreement with one obtained experimentally by quenching. The results of 3-D calculations are compared with previous 2- D findings. A video film featuring 3-D melt convection will be presented.

Bune, Andris V.↗
NASA NTRS1993

Comparison of Numerical Model Results with Diffusion Flames in Microgravity

The effects of gravity on methane diffusion flames were studied using a finite difference numerical model. Variables under consideration included velocity, pressure, temperature, enthalpy, reactive species, and inert carrier gas. Results obtained showed that flames in zero gravity were wider and taller than those in normal gravity. The use of a six reaction scheme produced similar predictions of flame width and height compared to those of the single reaction case. The numerical models predicted a considerable difference in the flame base region between normal gravity and low gravity. This region is considered to be beyond the boundaries of current analytical models.

Hyer, Paul V.↗
NASA NTRS1991

Net diffusivity in ocean general circulation models with nonuniform grids

The numerical vertical diffusivity K(num), embedded in a numerical ocean general circulation model with nonuniform vertical grid, is estimated. It is shown that in a downwelling region, K(num) is negative for a grid with grid size increasing with depth. When the grid size increment, or the downward vertical velocity, is large, K(num) may exceed the vertical diffusivity specified and may result in a negative effective vertical diffusivity. Therefore care needs to be taken to specify the vertical diffusivity in a numerical model with nonuniform grid, and a lower bound is generally imposed in order to avoid an unphysical negative value. Some possible effects of the negative effective diffusivity are discussed.

Yin, F. L.↗
NASA NTRS1995

On the Dynamics of Some Discretizations of Convection-Diffusion Equations

Numerical discretizations of differential equations which model physical processes can possess dynamics quite different from that of the equations themselves. Recently the emphasis has been on the the dynamics of numerical discretizations for Ordinary Differential Equations (ODEs). For Partial Differential Equations (PDEs) using a method of lines approach the situation is more complex. First, the spatial discretisation may introduce dynamics not present in the original equations; second, the solution of the resulting system of ODEs is open to the modified dynamics of the ODE solver used. These two effects may interact in a complex manner. In this talk we present some results of our recent work on the dynamics of discretizations of convection-diffusion equations, including those produced using Total Variation Diminishing (TVD) schemes and adaptive grid techniques. A more general overview of the area may be found on our accompanying poster presentation.

Sweby, Peter K.↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

Numerical simulation of diffusion-controlled droplet growth Dynamical correlation effects

Diffusion-controlled coarsening (Ostwald ripening) of precipitated solutions is studied by numerical simulation. An algorithm is devised which exploits the screening of solute concentration fields, thereby removing the restriction to small systems of previous work. Simulation of the coarsening of 5000 droplets at 10-percent volume fraction reveals long-ranged dynamical correlations which broaden the droplet size-distribution function and increase the coarsening-rate coefficient.

Beenakker, C. W. J.↗
DOE OSTI2020

Calculating fluctuations and self-correlations numerically for causal charge diffusion in relativistic heavy-ion collisions

Here, we study the propagation and diffusion of electric charge fluctuations in the Bjorken hydrodynamic model with both white and Catteneo noise using purely numerical methods. We show that a lattice of noise fluctuations is required to fully calculate the two-point correlators of charge. We introduce a numerical procedure to solve the stochastic differential equations that arise from the charge conservation equation on the lattice event by event. We explicitly identify the self-correlation term in the case of Catteneo noise and provide a physical interpretation. We provide a numerical recipe to remove this contribution from the full two-point correlators. Finally, we calculate the balance functions for charged hadrons. By limiting the speed of signal propagation, we observe the expected narrowing of the balance functions after removing the self-correlations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1981

Numerical modeling of diffusive-convective physical vapor transport in cylindrical vertical ampoules

Diffusive-convective physical vapor transport (PVT) in cylindrical, vertical ampoules of aspect ratio (length/radius) between 0.5 and 10 was modeled numerically. The transport of a crystal forming component through an inert component that undergoes zero net transport was considered. Systems were treated in which: (1) with unequal molecular weight of the components and with temperature gradients typically employed in PVT, convective flow arises dominantly from solutal density gradients; and (2) with equal molecular weight of the components, convective flow can arise only from thermal expansion. It was found that, due to the diffusion-induced horizontal density gradients, buoyancy-driven convective flows are superimposed on the diffusive-advective fluxes without threshold. Net recirculation sets in adjacent to the growing interface, in contrast to the corresponding monocomponent situation where marginally stable convective modes fill the whole fluid space. Depending on the orientation of the main transport direction with respect to gravity, convection can either reduce or enhance the diffusion-induced radial concentration gradients. Significant enhancement of the net transport rate was found to occur only when the whole vapor space between source and growing crystal is filled by a convective recirculation roll. Solutal and thermal convection results are similar; yet for quantitative discussions, thermal and solutal Rayleigh numbers are not interchangeable in contrast to convective situations that lack net mass transport across the fluid space.

Markham, B. L.↗
NASA NTRS2004

Scattering of laser light - more than just smoke and mirrors

A short course on off-beam cloud lidar is given. Specific topics addressed include: motivation and goal of off-beam cloud lidar; diffusion physics; numeric amalysis; and validity of the diffusion approximation. A demo of the process is included.

Davis, Anthony B.↗
DOE OSTI2023

The Impact of Circumsolar Diffuse Radiation on the Numerical Computation and Forecasting of DNI

Weather Research and Forecasting model with solar extensions (WRF-Solar) uses the Fast All-sky Radiation Model for Solar applications (FARMS) to predict solar radiation from the forecasted atmospheric gases, aerosols, and clouds. The Beer-Bouguer-Lambert law utilized by FARMS as well as other radiative transfer models assumes Direct Normal Irradiance (DNI) is a narrow beam only covering the sun disk. This assumption is interpreted differently in solar observations by pyrheliometers where the circumsolar diffuse radiation is accounted. This study precisely computes circumsolar diffuse radiation in all-sky conditions using a radiative transfer model based on a parameterization of precomputed cloud transmittance and reflectance. The model is implemented in WRF-Solar to provide day-ahead DNI forecast in the north America. The computation and forecasting of DNI is compared with the Beer-Bouguer-Lambert law to understand the impact of circumsolar diffuse radiation.

aerosols↗
DOE OSTI2022

Error analysis of numerical methods for thick diffusive neutron transport problems on Shishkin mesh

A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1995

Velocity Fields of Axisymmetric Hydrogen-Air Counterflow Diffusion Flames from LDV, PIV, and Numerical Computation

Laminar fuel-air counterflow diffusion flames (CFDFs) were studied using axisymmetric convergent-nozzle and straight-tube opposed jet burners (OJBs). The subject diagnostics were used to probe a systematic set of H2/N2-air CFDFs over wide ranges of fuel input (22 to 100% Ha), and input axial strain rate (130 to 1700 Us) just upstream of the airside edge, for both plug-flow and parabolic input velocity profiles. Laser Doppler Velocimetry (LDV) was applied along the centerline of seeded air flows from a convergent nozzle OJB (7.2 mm i.d.), and Particle Imaging Velocimetry (PIV) was applied on the entire airside of both nozzle and tube OJBs (7 and 5 mm i.d.) to characterize global velocity structure. Data are compared to numerical results from a one-dimensional (1-D) CFDF code based on a stream function solution for a potential flow input boundary condition. Axial strain rate inputs at the airside edge of nozzle-OJB flows, using LDV and PIV, were consistent with 1-D impingement theory, and supported earlier diagnostic studies. The LDV results also characterized a heat-release hump. Radial strain rates in the flame substantially exceeded 1-D numerical predictions. Whereas the 1-D model closely predicted the max I min axial velocity ratio in the hot layer, it overpredicted its thickness. The results also support previously measured effects of plug-flow and parabolic input strain rates on CFDF extinction limits. Finally, the submillimeter-scale LDV and PIV diagnostics were tested under severe conditions, which reinforced their use with subcentimeter OJB tools to assess effects of aerodynamic strain, and fueVair composition, on laminar CFDF properties, including extinction.

Pellett, Gerald L.↗
NASA NTRS1982

Analytical calculation of a single jet in crossflow and comparison with experiment

A series of calculations of a jet in crossflow using a three-dimensional finite difference model of the Navier-Stokes equations were made on a series of progressively finer grids. With a reasonable number of grid point (40x30x20), calculated jet penetration and mixing characteristics were found to compare favorably with the experimental measurements of Crabb, Durao and Whitelaw. The calculated results were grid dependent (i.e., numerical or false diffusion was present in the result). A finer grid calculation indicated that turbulence model deficiencies may become more noticeable in the calculated results as the magnitude of numerical diffusion is reduced.

Clauss, R. W.↗