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NASA NTRS2017

Tortuosity Computations of Porous Materials using the Direct Simulation Monte Carlo

Low-density carbon fiber preforms, used as thermal protection systems (TPS) materials for planetary entry systems, have permeable, highly porous microstructures consisting of interlaced fibers. Internal gas transport in TPS is important in modeling the penetration of hot boundary-layer gases and the in-depth transport of pyrolysis and ablation products. The gas effective diffusion coefficient of a porous material must be known before the gas transport can be modeled in material response solvers; however, there are very little available data for rigid fibrous insulators used in heritage TPS.The tortuosity factor, which reflects the efficiency of the percolation paths, can be computed from the effective diffusion coefficient of a gas inside a porous material and is based on the micro-structure of the material. It is well known, that the tortuosity factor is a strong function of the Knudsen number. Due to the small characteristic scales of porous media used in TPS applications (typical pore size of the order of 50 micron), the transport of gases can occur in the rarefied and transitional regimes, at Knudsen numbers above 1. A proper way to model the gas dynamics at these conditions consists in solving the Boltzmann equation using particle-based methods that account for movement and collisions of atoms and molecules.In this work we adopt, for the first time, the Direct Simulation Monte Carlo (DSMC) method to compute the tortuosity factor of fibrous media in the rarefied regime. To enable realistic simulations of the actual transport of gases in the porous medium, digitized computational grids are obtained from X-ray micro-tomography imaging of real TPS materials. The SPARTA DSMC solver is used for simulations. Effective diffusion coefficients and tortuosity factors are obtained by computing the mean-square displacement of diffusing particles.We first apply the method to compute the tortuosity factors as a function of the Knudsen number for computationally designed materials such as random cylindrical fibers and packed bed of spheres with prescribed porosity. Results are compared to literature values obtained using random walk methods in the rarefied and transitional regime and a finite-volume method for the continuum regime. We then compute tortuosity factors for a real carbon fiber material with a transverse isotropic structure (FiberForm), quantifying differences between through-thickness and in-plain tortuosities at various Knudsen regimes.

Tortuosity↗

NASA NTRS1994

Second-order closure PBL model with new third-order moments: Comparison with LES data

This paper contains two parts. In the first part, a new set of diagnostic equations is derived for the third-order moments for a buoyancy-driven flow, by exact inversion of the prognostic equations for the third-order moment equations in the stationary case. The third-order moments exhibit a universal structure: they all are a linear combination of the derivatives of all the second-order moments, bar-w(exp 2), bar-w theta, bar-theta(exp 2), and bar-q(exp 2). Each term of the sum contains a turbulent diffusivity D(sub t), which also exhibits a universal structure of the form D(sub t) = a nu(sub t) + b bar-w theta. Since the sign of the convective flux changes depending on stable or unstable stratification, D(sub t) varies according to the type of stratification. Here nu(sub t) approximately equal to wl (l is a mixing length and w is an rms velocity) represents the 'mechanical' part, while the 'buoyancy' part is represented by the convective flux bar-w theta. The quantities a and b are functions of the variable N(sub tau)(exp 2), where N(exp 2) = g alpha derivative of Theta with respect to z and tau is the turbulence time scale. The new expressions for the third-order moments generalize those of Zeman and Lumley, which were subsequently adopted by Sun and Ogura, Chen and Cotton, and Finger and Schmidt in their treatments of the convective boundary layer. In the second part, the new expressions for the third-order moments are used to solve the ensemble average equations describing a purely convective boundary laye r heated from below at a constant rate. The computed second- and third-order moments are then compared with the corresponding Large Eddy Simulation (LES) results, most of which are obtained by running a new LES code, and part of which are taken from published results. The ensemble average results compare favorably with the LES data.

Canuto, V. M.↗

NASA NTRS1977

A model for microwave intensity propagation in an inhomogeneous medium

A combined analytic and phenomenological approach, utilizing Maxwell's equations in the Born approximation with radiative transfer theory, is used to describe the propagation of microwave intensity in a scattering medium characterized by three-dimensional random fluctuations in refractive index, as well as nonrandom variations in permittivity, temperature, and loss. This approach yields microwave intensities as a function of polarization, direction, and position. Numerical techniques are presented to solve the transport equations, which include cases of spatially varying coefficients, and highly peaked phase functions. Some computed results illustrating the behavior of microwave intensity in various media are presented. Included are the angular and frequency spectra of thermal emission from semi-infinite media, and the diffuse transmission and reflection response of a scattering layer. The effects of scatterer geometry and scale sizes; correlation function; and gradients in temperature, loss, and scattering parameters are also demonstrated. This model should be particularly useful in interpreting active and passive remote sensing data.

Fisher, A. D.↗

NASA NTRS1978

Some relationships between Secchi depth and inherent optical properties of natural waters

Relationships between the inherent and optical properties of the ocean (Gorden et al., 1975 and Preisendorfer, 1961) are combined with the Duntley-Preisendorfer equation to show the dependence of these properties on the depth at which a Secchi disk disappears from view. An expression relating the Secchi depth to the limiting contrast of the disk is derived in terms of the average beam attenuation coefficient, the average diffuse attenuation coefficient for downwelling irradiance, the albedo of the disk, and the reflectance functions at the Secchi depth and just below the surface. It is shown that combining Secchi depth observations with other optical properties yields significant information about the constituents of the medium.

Gordon, H. R.↗

NASA NTRS1989

Merging of aircraft vortex trails - Similarities to magnetic field merging

This paper discusses the phenomenological and formal similarities between the merging of aircraft vortex trails and the merging of magnetic field lines in a plasma. High-resolution photographs are shown of smoke trails from the wing tips of an airplane. These photographs show that the two vortex trails merge together downstream of the aircraft in a way similar to the merging of oppositely directed magnetic field lines in a plasma. Although there are some differences, this correspondence is apparently related to the fact that the vorticity equation in a fluid has the same mathematical form as the magnetic field equation in an MHD plasma. In both cases the merging proceeds at a rate considerably faster than would be predicted from classical estimates of the viscosity and resistivity. The enhanced merging rate in the fluid case appears to result from turbulence that increases the diffusion rate in the merging region.

Gurnett, Donald A.↗

NASA NTRS1989

Synchrotron radiation from Neptune - Neptune's magnetic field and electron population

On the basis of radio measurements of Neptune at 20 cm, one can infer the presence of about 0.4 mJy synchrotron radiation. By assuming a dipole-like magnetic field, with the energetic electrons confined to the magnetic equator, Neptune's magnetic dipole moment is estimated. Its electron population should be between that in Uranus' and Jupiter's magnetospheres. If the electrons are injected by the solar wind, local acceleration processes in the magnetosphere are required to energize the particles, because adiabatic diffusion alone is not sufficient.

De Pater, Imke↗

NASA NTRS1990

Chemical heterogeneity and imperfect mixing in the solar nebula

The 'standard' accretion-disk model of the solar nebula is examined together with its basic equations, which are solved for the steady-state case. It is shown that, for this model of the solar nebula, the efficiency of mixing the products of thermochemical processing from small to large disk radii depends not on the magnitude of the eddy diffusivity but only on the ratio k between the eddy diffusivity and the eddy viscosity. In most cases, this ratio k is probably of order of unity or less, implying that most of the solar nebula was not contaminated by the consequences of thermochemical equilibria that were established at 'small' disk radii. It is noted that, while this condition is almost certainly satisfied if the physical process responsible for viscosity is thermal convection or waves, it has uncertain validity during the early phases of disk evolution where accretion-induced shear instabilities may dominate.

Stevenson, David J.↗

NASA NTRS1991

Heat Transfer to a Thin Solid Combustible in Flame Spreading at Microgravity

The heat transfer rate to a thin solid combustible from an attached diffusion flame, spreading across the surface of the combustible in a quiescent, microgravity environment, was determined from measurements made in the drop tower facility at NASA-Lewis Research Center. With first-order Arrhenius pyrolysis kinetics, the solid-phase mass and energy equations along with the measured spread rate and surface temperature profiles were used to calculate the net heat flux to the surface. Results of the measurements are compared to the numerical solution of the complete set of coupled differential equations that describes the temperature, species, and velocity fields in the gas and solid phases. The theory and experiment agree on the major qualitative features of the heat transfer. Some fundamental differences are attributed to the neglect of radiation in the theoretical model.

Bhattacharjee, S.↗

NASA NTRS1992

The gabbro-eclogite phase transition and the elevation of mountain belts on Venus

Among the four mountain belts surrounding Lakshmi Planum, Maxwell Montes is the highest and stands up to 11 km above the mean planetary radius and 7 km above Lakshmi Planum. The bulk composition and radioactive heat production of the crust on Venus, where measured, are similar to those of terrestrial tholeiitic basalt. Because the thickness of the low-density crust may be limited by the gabbro-garnet granulite-eclogite phase transitions, the 7-11 km maximum elevation of Maxwell Montes is difficult to understand except in the unlikely situation that the crust contains a large volume of magma. A possible explanation is that the base of the crust is not in phase equilibrium. It has been suggested that under completely dry conditions, the gabbro-eclogite phase transition takes place by solid-state diffusion and may require a geologically significant time to run to completion. Solid-state diffusion is a strongly temperature-dependent process. In this paper we solve the thermal evolution of the mountain belt to attempt to constrain the depth of the gabbro-eclogite transition and thus to assess this hypothesis quantitatively. The one-dimensional heat equation is solved numerically by a finite difference approximation. The deformation of the horizontally shortening crustal and mantle portions of the thermal boundary layer is assumed to occur by pure shear, and therefore the vertical velocity is given by the product of the horizontal strain rate and depth.

Namiki, Noriyuki↗

NASA NTRS2003

Vector Radiative Transfer Equation for Arbitrarily Shaped and Arbitrarily Oriented Particles: A Microphysical Derivation from Statistical Electromagnetics

We use the concepts of statistical electromagnetics to derive the general radiative transfer equation (RTE) describing multiple scattering of polarized light by sparse discrete random media consisting of arbitrarily shaped and arbitrarily oriented particles. The derivation starts from the volume integral and Lippmann-Schwinger equations for the electric field scattered by a fixed N-particle system and proceeds to the vector form of the Foldy-Lax equations and their approximate far-field version. We then assume that particle positions are completely random and derive the vector RTE by applying the Twersky approximation to the coherent electric field and the Twersky and ladder approximations to the coherency dyad of the diffuse field in the limit N -> infinity. The concluding section discusses the physical meaning of the quantities entering the general vector RTE and the assumptions made in its derivation.

Mishchenko, Michael I.↗

NASA NTRS1974

Diffusive ignition and combustion in a wall jet

Hydrogen is injected from a downstream facing step in a wall into a high-temperature stream. Temperature and hydroxyl radical concentration are measured downstream of the injection plane by means of ultraviolet absorption spectroscopy. The experimental results are compared with theory which is based on a finite-difference solution of boundary-layer equations. Finite-rate kinetics equations are included in the analysis. The analytic predictions are also compared with previously obtained experimental results which are based on probe measurements. Comparison is made between calculated and observed ignition distances.

Kurkov, A. P.↗

NASA NTRS1974

Diffusive ignition and combustion in a wall jet

Kurkov, A. P.↗

NASA NTRS1993

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper 24: A general approach to measuring the value of aerospace information products and services

This paper discusses the various approaches to measuring the value of information, first defining the meanings of information, economics of information, and value. It concludes that no general model of measuring the value of information is possible and that the usual approaches, such as cost/benefit equations, have very limited applications. It also concludes that in specific contexts with given goals for newly developed products and services or newly acquired information there is a basis for its objective valuation. The axioms and inputs for such a model are described and directions for further verification and analysis are proposed.

Brinberg, Herbert R.↗

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 NTRS1965

Diffusion of protons in the outer radiation belt.

Diffusion of protons in outer radiation belt due to violation of third adiabatic invariant for trapped particles

SOLAR WIND↗

NASA NTRS1972

Source and identification of heavy ions in the equatorial F layer.

Further evidence is presented to show that the interpretation of some Ogo 6 retarding potential analyzer (RPA) results in terms of ambient Fe+ ions is correct. The Fe+ ions are observed only within dip latitudes of plus or minus 30 deg, and the reason for this latitudinal specificity is discussed in terms of a low-altitude source region and F region diffusion and electrodynamic drift. It is shown that the polarization field associated with the equatorial electrojet will raise ions to 160 km out of a chemical source region below 100 km but it will do so only in a narrow region centered on the dip equator. Subsequent vertical ExB drift, coupled with motions along the magnetic fields, can move the ions to greater heights and greater latitudes. There should be a resultant fountain of metallic ions rising near the equator that subsequently descends back to the E and D layers at tropical latitudes.

Hanson, W. B.↗

NASA NTRS1975

A dynamic model for the time evolution of the modulated cosmic ray spectrum

A recently developed model predicts an energy dependent phase lag in the modulated cosmic ray density U(t) given by U(t) approximately equal to US (t - tau) where US is the solution to the Fokker-Planck equation under time independent conditions and tau is the average time spent by particles inside the modulating region. The delay times tau are functions of modulating parameters R (the radius of the modulating cavity), V (the solar wind velocity), and K (the effective average diffusion-coefficient which is a function of energy). This model is applied to predict the time evolution of the modulated cosmic ray proton spectrum over a simulated solar cycle. A modulation produced mostly by varying R over the solar cycle is less consistent with the observations.

Ogallagher, J. J.↗

NASA NTRS1987

Whistler mode emissions in the Uranian radiation belts

Voyager 2 detected intense whistler mode emissions and fluxes of energetic electrons during the outbound pass through the region of auroral L shells. The observed energetic (E greater than 22 keV) electron distribution, a model warm (E less than 27.5 keV) electron distribution, and the cold plasma density profile deduced by Kurth et al. (1987) are used to calculate the ray path-integrated spatial amplification of whistlers which arrive at Voyager 2 from the magnetic equator. By matching the calculated amplification and the relative gains at different frequencies deduced from the observed whistler power spectrum, the pitch angle anisotropy parameters of the electron distributions are determined to within a fairly narrow range of values. The estimated bounce average pitch angle diffusion coefficient indicates that electrons are on strong diffusion over a wide range in energies. The electron precipitation energy flux is sufficient to produce the observed auroral light emissions.

Coroniti, F. V.↗