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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Numerical Simulation of Combustion and Extinction of a Solid Cylinder in Low-Speed Cross Flow

The combustion and extinction behavior of a diffusion flame around a solid fuel cylinder (PMMA) in low-speed forced flow in zero gravity was studied numerically using a quasi-steady gas phase model. This model includes two-dimensional continuity, full Navier Stokes' momentum, energy, and species equations with a one-step overall chemical reaction and second-order finite-rate Arrhenius kinetics. Surface radiation and Arrhenius pyrolysis kinetics are included on the solid fuel surface description and a parameter Phi, representing the percentage of gas-phase conductive heat flux going into the solid, is introduced into the interfacial energy balance boundary condition to complete the description for the quasi-steady gas-phase system. The model was solved numerically using a body-fitted coordinate transformation and the SIMPLE algorithm. The effects of varying freestream velocity and Phi were studied. These parameters have a significant effect on the flame structure and extinction limits. Two flame modes were identified: envelope flame and wake flame. Two kinds of flammability limits were found: quenching at low-flow speeds due to radiative loss and blow-off at high flow speeds due to insufficient gas residence time. A flammability map was constructed showing the existence of maximum Phi above which the solid is not flammable at any freestream velocity.

Tien, J. S.↗
NASA NTRS1991

Discrete observability and numerical quadrature

The authors consider the problem of approximate observability of a one-dimensional diffusion equation on a finite spatial domain with spatial point measurements. The problem of the optimal selection of the measurement points is considered under three conditions: (1) no preassigned measurement nodes; (2) one preassigned node and; (3) two preassigned nodes. The main observation is that the optimal choice is related to three classical procedures in numerical analysis: (1) Gaussian quadrature; (2) Radau quadrature and; (3) Lobatto quadrature. It is shown that the existence of the Radau and Lobatto quadrature is closely related to classical root locus theory.

Martin, Clyde F.↗
NASA NTRS1973

Startup analysis for a high temperature gas loaded heat pipe

A model for the rapid startup of a high-temperature gas-loaded heat pipe is presented. A two-dimensional diffusion analysis is used to determine the rate of energy transport by the vapor between the hot and cold zones of the pipe. The vapor transport rate is then incorporated in a simple thermal model of the startup of a radiation-cooled heat pipe. Numerical results for an argon-lithium system show that radial diffusion to the cold wall can produce large vapor flow rates during a rapid startup. The results also show that startup is not initiated until the vapor pressure p sub v in the hot zone reaches a precise value proportional to the initial gas pressure p sub i. Through proper choice of p sub i, startup can be delayed until p sub v is large enough to support a heat-transfer rate sufficient to overcome a thermal load on the heat pipe.

Sockol, P. M.↗
NASA NTRS1988

Time scales for formation and spreading of velocity shells of pickup ions in the solar wind

This paper discusses the process of assimilation (pickup) by the solar wind of newly ionized atoms and molecules. Generally, the pickup process is considered to evolve in three stages: (1) the initial interaction of newly created ions with the interplanetary magnetic field to form the ring-beam distribution; (2) pitch angle scattering of the ring beam to form a hollow shell; and (3) slower velocity diffusion to form a partially filled-in shell distribution. Using numerical simulations of turbulence such as would occur naturally in the solar wind and such as would be encountered near cometary bow shocks, the processes of shell formation and evolution are studied, and the results are used to estimate the time scales for shell formation and diffusion in several situations of recent observational interest, the interstellar He data obtained by AMPTE and cometary ion pickup distributions obtained by various spacecraft at comets Giacobini-Zinner and Halley.

Gaffey, J. D., Jr.↗
NASA NTRS1985

Numerical Descriptions of Cosmic-Ray Transport

The behavior of energetic particles in the solar system is described by a well known Fokker-Planck equation. Although analytic methods yield insight into the nature of its solutions, especially in the diffusion regime, calculations that go beyond diffusion are very complicated. The reliability of these calculations is of concern, because numerical methods are notorious for their errors and artifacts. The well known Milne problem of classical transport theory was analyzed with the aid of three different numerical methods. These are: (1) The method of eigenfunctions in which the distribution function is approximated by a sum of eigenfunctions of the scattering operator, (2) Numerical solutions of a finite difference aquation; and (3) Direct simulation of the scattering and streaming of individual particles with the aid of Monte Carlo methods.

Earl, J. A.↗
NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗
NASA NTRS1960

Comparison of Turbulent Heat-Transfer Results for Uniform Wall Heat Flux and Uniform Wall Temperature

The purpose of this note is to examine in a more precise way how the Nusselt numbers for turbulent heat transfer in both the fully developed and thermal entrance regions of a circular tube are affected by two different wall boundary conditions. The comparisons are made for: (a) Uniform wall temperature (UWT); and (b) uniform wall heat flux (UHF). Several papers which have been concerned with the turbulent thermal entrance region problem are given. 1 Although these analyses have all utilized an eigenvalue formulation for the thermal entrance region there were differences in the choices of eddy diffusivity expressions, velocity distributions, and methods for carrying out the numerical solutions. These differences were also found in the fully developed analyses. Hence when making a comparison of the analytical results for uniform wall temperature and uniform wall heat flux, it was not known if differences in the Nusselt numbers could be wholly attributed to the difference in wall boundary conditions, since all the analytical results were not obtained in a consistent way. To have results which could be directly compared, computations were carried out for the uniform wall temperature case, using the same eddy diffusivity, velocity distribution, and digital computer program employed for uniform wall heat flux. In addition, the previous work was extended to a lower Reynolds number range so that comparisons could be made over a wide range of both Reynolds and Prandtl numbers.

Siegel, R.↗
NASA NTRS1991

Convective instability in superposed fluid and anisotropic porous layers

The onset of thermal convection due to heating from below in a system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity is studied. The linear perturbation equations are solved numerically. It is found that the effects of anisotropy on the onset of thermal convection are most profound for small values of the depth ratio xi (ratio of fluid layer thickness to porous layer thickness), since in that case, the onset of convection corresponds to significant motion in both layers. For fixed vlues of the vertical permeability in the porous medium, decreasing the value of zeta (ratio of horizontal to vertical permeability) leads to stabilization of the superposed layer configuration because of increased resistance to motion in the porous medium. For larger values of xi, the onset of motion is increasingly confined to the fluid layer, with the transport of heat through the porous layer occurring primarily by conduction. Accordingly, the influence of zeta on the stability characteristics for larger xi is less significant than the effects of an anisotropic thermal conductivity.

Chen, Falin↗
NASA NTRS1991

A study of hydrogen diffusion flames using PDF turbulence model

The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

Hsu, Andrew T.↗
NASA NTRS1990

Fast secant methods for the iterative solution of large nonsymmetric linear systems

A family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.

Deuflhard, Peter↗
NASA NTRS1992

Quasi-linear velocity space diffusion of heavy cometary pickup ions on bispherical diffusion characteristics

We consider an ion transport equation describing the source, convection, adiabatic acceleration, and quasi-linear velocity diffusion of cometary pickup ions. The equation is solved numerically along solar wind plasma flow lines for the environment of Comet Halley, to obtain distributions at positions on the Giotto spacecraft trajectory which may be compared with observations. We obtain full two-dimensional (pitch angle and velocity) numerical distributions which show pitch angle scattering about the wave scattering centers at +/- V(A), where V(A) is the Alfven wave speed in the solar wind frame. Peak ion phase-space densities approximately follow the bispherical shell geometry. The energy distributions F(v) agree well with Giotto observations at lower v, but in the high-energy tail there is evidence possibly for the first-order Fermi acceleration mechanism taking place in the Comet Halley foreshock region.

Huddleston, D. E.↗
NASA NTRS1995

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks

We investigate the asymptotic convergence of finite-difference schemes for the Euler equations when the limiting solution contains shocks. The Lax-Wendroff theorem guarantees that certain conservative schemes converge to correct, physically valid solutions. We focus on two one-dimensional operator-split schemes with explicit artificial-viscosity terms. One, an internal-energy scheme, does not satisfy the assumptions of Lax-Wendroff; the other, a conservative total-energy scheme, does. With viscous lengths chosen proportional to the grid size, we find that both schemes converge to their zero-grid-size limits at the theoretically expected rate, but only the conversative scheme converges toward correct solutions of the inviscid fluid equations. We show that the difference in their behaviors results directly from the presence of shocks in the limiting solution. Empirically, we find that when the viscous lenghts tend toward zero more slowly than the grid size, however the nonconservative scheme also converges toward correct solutions. We characterize the asymptotic behavior of the total-energy scheme in a particular problem in which a shock forms. As the grid is refined, a Cauchy error approaches the expected rate of change slowly. We show that the changes in the artificial viscosity alter the diffusion of small-amplitude waves. The differences associated with such waves make the dominant contribution to the Cauchy error. We formulate an analytic model to relate the rate of approach to the effect of varying diffusion in waves and find quantitative agreement with our numerical results.

Kimoto, Paul A.↗
NASA NTRS1995

On the upstream boundary of electron foreshocks in the solar wind

The upstream boundary of electron foreshocks is defined as the path of the fastest electrons reflected by collisionless shocks and moving along the magnetic field in the solar wind. Considerable levels of magnetic fluctuations are found in these regions of the solar wind, and their effect is to create both a broadening and a fine structure of the electron foreshock boundary. The magnetic structure is studied by means of a 3-D numerical simulation of a turbulent magnetic field. Enhanced, anomalous diffusion is found, (Delta x(exp 2)) varies as s(sup alpha), where alpha is greater than 1 for typical values of the parameters (here, Delta x(exp 2) is the mean square width of the tangent magnetic surface and s is the field line length). This corresponds to a Levy flight regime for the magnetic field line random walk, and allows very efficient electron propagation perpendicular to the magnetic field. Implications on the observations of planetary foreshocks and of the termination shock foreshock are considered.

Zimbardo, G.↗
NASA NTRS1996

Multigrid Techniques for Highly Indefinite Equations

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Shapira, Yair↗
NASA NTRS1999

Step Bunching: Influence of Impurities and Solution Flow

Step bunching results in striations even at relatively early stages of its development and in inclusions of mother liquor at the later stages. Therefore, eliminating step bunching is crucial for high crystal perfection. At least 5 major effects causing and influencing step bunching are known: (1) Basic morphological instability of stepped interfaces. It is caused by concentration gradient in the solution normal to the face and by the redistribution of solute tangentially to the interface which redistribution enhances occasional perturbations in step density due to various types of noise; (2) Aggravation of the above basic instability by solution flowing tangentially to the face in the same directions as the steps or stabilization of equidistant step train if these flows are antiparallel; (3) Enhanced bunching at supersaturation where step velocity v increases with relative supersaturation s much faster than linear. This v(s) dependence is believed to be associated with impurities. The impurities of which adsorption time is comparable with the time needed to deposit one lattice layer may also be responsible for bunching; (4) Very intensive solution flow stabilizes growing interface even at parallel solution and step flows; (5) Macrosteps were observed to nucleate at crystal corners and edges. Numerical simulation, assuming step-step interactions via surface diffusion also show that step bunching may be induced by random step nucleation at the facet edge and by discontinuity in the step density (a ridge) somewhere in the middle of a face. The corresponding bunching patterns produce the ones observed in experiment. The nature of step bunching generated at the corners and edges and by dislocation step sources, as well as the also relative importance and interrelations between mechanisms 1-5 is not clear, both from experimental and theoretical standpoints. Furthermore, several laws controlling the evolution of existing step bunches have been suggested, though unambiguous conclusions are still missing. Addressing these issues is the major goal of the present project. The theory addressing the above problem, experimental methods, several figures which include: (1) the spatial wave numbers at which the system is neutrally stable as a function of growth velocity for linear kinetics and supersaturation for nonlinear kinetics; (2) a schematic of the experiment of lysozyme crystal growing under conditions of natural convection; (3) fluctuations in time, t, of the normal growth rate, R(t), vicinal slope, p(t) and Fourier Spectra of R(t), discussions and conclusions are presented.

Chernov, A. A.↗
NASA NTRS1999

Advanced Electromagnetic Methods for Aerospace Vehicles

The imminent destructive threats of Lightning on helicopters and other airborne systems has always been a topic of great interest to this research grant. Previously, the lightning induced currents on the surface of the fuselage and its interior were predicted using the finite-difference time-domain (FDTD) method as well as the NEC code. The limitations of both methods, as applied to lightning, were identified and extensively discussed in the last meeting. After a thorough investigation of the capabilities of the FDTD, it was decided to incorporate into the numerical method a subcell model to accurately represent current diffusion through conducting materials of high conductivity and finite thickness. Because of the complexity of the model, its validity will be first tested for a one-dimensional FDTD problem. Although results are not available yet, the theory and formulation of the subcell model are presented and discussed here to a certain degree. Besides lightning induced currents in the interior of an aircraft, penetration of electromagnetic fields through apertures (e.g., windows and cracks) could also be devastating for the navigation equipment, electronics, and communications systems in general. The main focus of this study is understanding and quantifying field penetration through apertures. The simulation is done using the FDTD method and the predictions are compared with measurements and moment method solutions obtained from the NASA Langley Research Center. Cavity-backed slot (CBS) antennas or slot antennas in general have many applications in aircraft-satellite type of communications. These can be flushmounted on the surface of the fuselage and, therefore, they retain the aerodynamic shape of the aircraft. In the past, input impedance and radiation patterns of CBS antennas were computed using a hybrid FEM/MoM code. The analysis is now extended to coupling between two identical slot antennas mounted on the same structure. The predictions are performed using both the hybrid FEM/MoM and the FDTD NEWS code. The results are compared with each other as well as with measurements performed in the ElectroMagnetic Anechoic Chamber (EMAC) of ASU. In addition to self and mutual impedances versus frequency, the comparisons include mutual coupling S(sub 12) as a function of distance for various slot orientations.

Balanis, Constantine A.↗