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NASA NTRS2008

Effects of C/O Ratio and Temperature on Sooting Limits of Spherical Diffusion Flames

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, residence time and scalar dissipation rate. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with scalar dissipation rate lower than 2/s were found to have temperatures near 1400 K where C/O = 0.51, whereas flames with greater scalar dissipation rate required increased temperatures. This finding was valid across a broad range of fuel and oxidizer compositions and convection directions.

Lecoustre, V. R.↗

NASA NTRS1987

Fast-dynamo action in unsteady flows and maps in three dimensions

Unsteady fast-dynamo action is obtained in a family of stretch-fold-shear maps applied to a spatially periodic magnetic field in three dimensions. Exponential growth of a mean field in the limit of vanishing diffusivity is demonstrated by a numerical method which alternates instantaneous deformations with molecular diffusion over a finite time interval. Analysis indicates that the dynamo is a coherent feature of the large scales, essentially independent of the cascade of structure to small scales.

Bayly, B. J.↗

NASA NTRS1982

On the energy dependence of the radial diffusion coefficient and spectra of inner radiation belt particles - Analytic solutions and comparison with numerical results

A theoretical method by which the energy dependence of the radial diffusion coefficient may be deduced from spectral observations of the particle population at the inner edge of the earth's radiation belts is presented. This region has previously been analyzed with numerical techniques; in this report an analytical treatment that illustrates characteristic limiting cases in the L shell range where the time scale of Coulomb losses is substantially shorter than that of radial diffusion (L approximately 1-2) is given. It is demonstrated both analytically and numerically that the particle spectra there are shaped by the energy dependence of the radial diffusion coefficient regardless of the spectral shapes of the particle populations diffusing inward from the outer radiation zone, so that from observed spectra the energy dependence of the diffusion coefficient can be determined. To insure realistic simulations, inner zone data obtained from experiments on the DIAL, AZUR, and ESRO 2 spacecraft have been used as boundary conditions. Excellent agreement between analytic and numerical results is reported.

Westphalen, H.↗

NASA NTRS1991

Sinc-Galerkin estimation of diffusivity in parabolic problems

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

Smith, Ralph C.↗

NASA NTRS1973

Behavior of nitric oxide formed by the space shuttle in the mesosphere

A numerical model of eddy diffusive transport of emitted gases from the space shuttle wake, including chemical reactions between the emitted constituents and the ambient atmosphere, has been constructed for 75 km altitude. The numerical methods involve explicit solution of the diffusion equation and Runge-Kutta method for the chemical reactions. The time required to reach background levels of nitric oxide concentration of 7 x 10 to the 7th power molecules/cc has been calculated. This relaxation time depends strongly on atmospheric conditions.

Eberstein, I. J.↗

NASA NTRS1992

Numerical simulation of conservation laws

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Chang, Sin-Chung↗

NASA NTRS1992

Systematic study of Reynolds stress closure models in the computations of plane channel flows

The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.

Demuren, A. O.↗

NASA NTRS1993

Perspective - Systematic study of Reynolds stress closure models in the computations of plane channel flows

Demuren, A. O.↗

NASA NTRS1999

Vortex/Flame Interactions in Microgravity Pulsed Jet Diffusion Flames

The problem of vortex/flame interaction is of fundamental importance to turbulent combustion. These interactions have been studied in normal gravity. It was found that due to the interactions between the imposed disturbances and buoyancy induced instabilities, several overall length scales dominated the flame. The problem of multiple scales does not exist in microgravity for a pulsed laminar flame, since there are no buoyancy induced instabilities. The absence of buoyant convection therefore provides an environment to study the role of vortices interacting with flames in a controlled manner. There are strong similarities between imposed and naturally occurring perturbations, since both can be described by the same spatial instability theory. Hence, imposing a harmonic disturbance on a microgravity laminar flame creates effects similar to those occurring naturally in transitional/turbulent diffusion flames observed in microgravity. In this study, controlled, large-scale, axisymmetric vortices are imposed on a microgravity laminar diffusion flame. The experimental results and predictions from a numerical model of transient jet diffusion flames are presented and the characteristics of pulsed flame are described.

Bahadori, M. Y.↗

NASA NTRS1984

Estimation of vertical diffusion from observations of Atmospheric turbulence layers, part 4.4B

There have been numerous studies addressing the turbulent diffusion in the stratosphere and mesosphere during the last two decades. The motivation for such studies was the need for an understanding of the thermal and constituent structure of the middle atmosphere. Observational estimates of the horizontal and/or vertical diffusion were obtained using chemical release, rocket vapor trail, aircraft, balloon, and radar techniques. During the same period, a number of theoretical studies were performed to infer the level of vertical diffusion needed to account for observed constituent profiles. There appears to be a discrepancy between the level of vertical diffusion required for the dissipation of gravity wave and tidal motions on the one hand and for the maintenance of observed temperature and constituent profiles on the other. A possible explanation of this discrepancy is outlined. Measurements that may help verify this explanation are suggested.

Fritts, D. C.↗

NASA NTRS1982

A numerical simulation of the magnetospheric gate model for the X-ray bursters

A Lagrangian, stellar interior computer code which assumes radiation transport by diffusion is used to numerically simulate an X-ray burst occurring on a rapidly rotating, 1 solar mass neutron star accreting material from a companion in noncontinuous, episodic fashion. The blob of gas from the companion extends from the surface of the neutron star to a radius of 185 km, is optically thick, has mass of 10 to the -11th solar masses, and is initially at rest with respect to the surface. The gas initially has a temperature of about 10 million K and a surface luminosity of 0.1 that of the sun. The infall results in a burst which lasts about 0.1 second and reaches a peak luminosity and effective temperature of 240,000 suns and nine million K. The burst is followed by a phase of oscillations with a period of 0.2 second. It is found that the burst is too cool and rapid to resemble normal bursts, although the time scale is in agreement with some observations.

Starrfield, S.↗

NASA NTRS1993

Multilevel methods for transport equations in diffusive regimes

We consider the numerical solution of the single-group, steady state, isotropic transport equation. An analysis by means of the moment equations shows that a discrete ordinate S(sub N) discretization in direction (angle) with a least squares finite element discretization in space does not behave properly in the diffusion limit. A scaling of the S(sub N) equations is introduced so that the least squares discretization has the correct diffusion limit. For the resulting discrete system a full multigrid algorithm was developed.

Manteuffel, Thomas A.↗

NASA NTRS1987

Numerical studies of the thermal design sensitivity calculation for a reaction-diffusion system with discontinuous derivatives

The aim of this study is to find a reliable numerical algorithm to calculate thermal design sensitivities of a transient problem with discontinuous derivatives. The thermal system of interest is a transient heat conduction problem related to the curing process of a composite laminate. A logical function which can smoothly approximate the discontinuity is introduced to modify the system equation. Two commonly used methods, the adjoint variable method and the direct differentiation method, are then applied to find the design derivatives of the modified system. The comparisons of numerical results obtained by these two methods demonstrate that the direct differentiation method is a better choice to be used in calculating thermal design sensitivity.

Hou, Jean W.↗

NASA NTRS1989

New insights in the photochemistry of grain mantles: The identification of the 4.62 and 6.87 micron bands

The mid-IR spectral region of molecular clouds is known to show the fingerprints of molecules frozen in the icy mantles of the interstellar grains. To study the complex chemical and physical interactions on the ice mantles accreted on grains in molecular clouds numerous UV irradiation and diffusion experiments were performed. The irradiation of binary ices was studied. Using isotopic labelling on NH3/CO and NH3/O2 ices numerous compounds were identified, of which OCN(-), NO2(-), NO3(-), and NH4(+) ions reveal a new type of chemical reactions. It appeared that these compounds were formed by proton transfer reactions induced by the interaction between an acid (HNCO, HNO2, HNO3) and a base (NH3) through a hydrogen bond. This mechanism was confirmed by a study of photolyzed diluted argon mixtures. The main astrophysically relevant data from the overall study are presented. The 4.62 micron band in W33A can be reproduced with NH3/CO containing irradiated ices and was identified with OCN(-). The 6.87 micron band in W33A and other photostellar objects is reproduced with NH3/O2 containing ices and is identified with NH4(+).

Grim, Ruud↗

NASA NTRS1979

Magnetic diffusion and ionization fractions in dense molecular clouds - The role of charged grains

The physics of magnetic diffusion in dense molecular clouds is examined, with particular attention given to the role of charged grains in controlling the process. The ionization fraction of dense molecular clouds in the presence of grains is determined from considerations of charge exchange, dissociative recombination, radiative recombination and collisions between grains and charged species, and it is found that the inclusion of grains tends to lower the ionization fraction for a given cosmic-ray ionization rate and metal depletion. The kinematics of grain motion is discussed and it is shown that at temperatures less than 30 K, each grain alternates rapidly in charge between -1 and 0 and thus executes periodic motion in a self-gravitating cloud containing a magnetic field. The full kinematics of magnetic diffusion including the motions of ions and electrons are then examined, taking into account the additional viscous force from charged grains, and numerical calculations of the diffusion time scales of uniform, magnetically supported clouds or cloud cores are presented.

Elmegreen, B. G.↗

NASA NTRS1997

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bune, Andris V.↗

NASA NTRS2001

Numerical Study of g-Jitter Induced Double-Diffusive Convection

A finite element study is presented of double-diffusive convection driven by g-jitter in a microgravity environment. Mathematical formulations are presented and extensive simulations are carried out for g-jitter induced fluid flow, temperature distribution, and solutal transport in an alloy system under consideration for space flights. Computations include the use of idealized single-frequency and multi-frequency g-jitter as well as the real g-jitter data taken during an actual Space Shuttle fight. Little correlation is seen between these velocity components for the g-jitter components studied. The temperature field is basically undisturbed by convection because of a small Pr number for the fluid. The disturbance of the concentration field, however, is pronounced, and the local variation of the concentration follows the velocity oscillation in time. It is found that although the concentration field varies in both position and time, the local concentration gradient remains approximately constant in time. Numerical study further indicates that with an increase in g-jitter force (or amplitude), the nonlinear convective effects become much more obvious, which in turn drastically change the concentration fields. The simulated results computed using the g-jitter data taken during space flights show that both the velocity and concentration become random, following approximately the same pattern as the g-jitter perturbations.

Shu, Y.↗

NASA NTRS1994

An experimental and theoretical study of radiative extinction of diffusion flames

Our work was primarily theoretical and numerical. We investigated the simplified modeling of heat losses in diffusion flames, then we 'ramped up' the level of complexity in each successive study until the final chapter discussed the general problem of soot/flame interaction. With regard to the specific objective of studying radiative extinction, we conclude that in the steady case a self-extinguishing zero-g flame is unlikely to occur. The soot volume fractions are too small. On the other hand, our work does provide rational means for assessing the mixture of chemical energy release and radiative heat release. It also provides clues for suitable 'tailoring' this balance. Thus heat fluxes to surrounding surfaces can be substantially increased by exploiting and modifying its sooting capability.

Wichman, Indrek S.↗