Radiative transfer by doubling very thin layers.
Radiative transfer by doubling very thin layers in problem of diffuse reflection from plane-parallel atmosphere eliminates numerically solving transfer equation
Hansen, J. E.↗
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Effective slip coefficients for coupled conduction-radiation problems.
Combined conduction and radiation transfer equations solutions for absorbing-emitting gas, obtaining slip coefficient for diffusion solution correct boundary condition
Goldstein, M. E.↗
Comments on ""Contact Diffusion Interaction of Materials with Cladding''
A Russian paper by A. A. Babad-Zakhryapina contributes much to the understanding of fuel, clad interactions, and thus to nuclear thermionic technology. In that publication the basic diffusion expression is a simple one. A more general but complicated equation for this mass transport results from the present work. With appropriate assumptions, however, the new relation reduces to Babad-Zakhryapina's version.
Morris, J. F.↗
Fission-gas release from uranium nitride at high fission rate density
A sweep gas facility has been used to measure the release rates of radioactive fission gases from small UN specimens irradiated to 8-percent burnup at high fission-rate densities. The measured release rates have been correlated with an equation whose terms correspond to direct recoil release, fission-enhanced diffusion, and atomic diffusion (a function of temperature). Release rates were found to increase linearly with burnups between 1.5 and 8 percent. Pore migration was observed after operation at 1550 K to over 6 percent burnup.
Weinstein, M. B.↗
Experimental determination of turbulence in a GH2-GOX rocket combustion chamber
The intensity of turbulence and the Lagrangian correlation coefficient for a gaseous rocket combustion chamber have been determined from the experimental measurements of the tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and Spalding's numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber. An exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the maximum value of the intensity of turbulence is about 15% and the Lagrangian correlation coefficient drops to about 0.12 in one inch of the chamber length.
Tou, P.↗
An extended classical solution of the droplet growth problem
Problems of applying the classical kinetic theory to the growth of small droplets from vapor are examined. A solution for the droplet growth equation is derived which is based on the assumption of a diffusive field extending to the drop surface. The method accounts for partial thermal and mass accommodation at the interface and the kinetic limit to the mass and heat fluxes, and it avoids introducing the artifact of a discontinuity in the thermal and vapor field near the droplet. Consideration of the environmental fields in spherical geometry utilizing directional fluxes yields boundary values in terms of known parameters and a new Laplace transform integral.
Anderson, B. J.↗
Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes
A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.
Palusinski, O. A.↗
Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface
Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.
Strelkov, S. A.↗
Assessment of discretization schemes to reduce numerical diffusion in the calculation of complex flows
Comprehensive criteria for evaluating finite-difference schemes to reduce numerical diffusion in the solution of the Reynolds averaged Navier-Stokes equations have been established in this study. Several candidate schemes have been examined, based on these criteria. Taylor series analyses, model problem studies and examination of the difference equations have been used to assess the schemes. Two schemes, which showed the most promise, and satisfied a majority of the criteria, are recommended for incorporation into two dimensional and three dimensional computer codes for further evaluation.
Syed, S. A.↗
Catalytic ignition model in a monolithic reactor with in-depth reaction
Two transient models have been developed to study the catalytic ignition in a monolithic catalytic reactor. The special feature in these models is the inclusion of thermal and species structures in the porous catalytic layer. There are many time scales involved in the catalytic ignition problem, and these two models are developed with different time scales. In the full transient model, the equations are non-dimensionalized by the shortest time scale (mass diffusion across the catalytic layer). It is therefore accurate but is computationally costly. In the energy-integral model, only the slowest process (solid heat-up) is taken as nonsteady. It is approximate but computationally efficient. In the computations performed, the catalyst is platinum and the reactants are rich mixtures of hydrogen and oxygen. One-step global chemical reaction rates are used for both gas-phase homogeneous reaction and catalytic heterogeneous reaction. The computed results reveal the transient ignition processes in detail, including the structure variation with time in the reactive catalytic layer. An ignition map using reactor length and catalyst loading is constructed. The comparison of computed results between the two transient models verifies the applicability of the energy-integral model when the time is greater than the second largest time scale of the system. It also suggests that a proper combined use of the two models can catch all the transient phenomena while minimizing the computational cost.
Tien, Ta-Ching↗
An experimental investigation of the separating/reattaching flow over a backstep
Transport characteristics of the turbulent kinetic energy, k, and the shear stream, bar(-uv), were studied in an incompressible boundary layer downstream of the reattachment of the separated flow behind a backward facing step. Hot-wire measurement techniques were used to measure three Reynolds stresses and higher order mean products of velocity fluctuations. These quantities were used to evaluate advection, turbulent diffusion, and production terms of the k and bar(-uv) transport equations. The dissipation rate and pressure-strain terms were obtained as the difference of all the other terms. The Reynolds number based on the step height was 37,000 and the upstream oncoming flow was fully developed turbulent boundary layer with the R(sub theta) = 3600.
Jovic, Srboljub↗
Numerical analysis of a vortex controlled diffuser
A numerical study of a prototypical vortex controlled diffuser is performed. The basic diffuser geometry consists of a step expansion in a pipe of area ratio 2.25:1. The incompressible Reynolds averaged Navier-Stokes equations, employing the K-epsilon turbulence model, are solved. Results are presented for bleed rates ranging from 1 to 7 percent. Diffuser efficiencies in excess of 80 percent are obtained. Reattachment lengths are reduced by a factor of up to 3. These results are in qualitative agreement with previous experimental work. However, differences in some basic details of experimentally observed and the present numerically generated flowfields exist. The effect of swirl is also investigated.
Spall, Robert E.↗
The resonance lines of MG2 as diagnostics of the upper solar chromosphere
The resonance lines of singly ionized magnesium, the MgII h&k lines at about 280 nm, are two of the small number of lines in the solar spectrum that are optically thick in the chromospheric part of the solar atmosphere. Potentially these lines contain information on the initial temperature rise that occurs at the top of the photosphere. Unfortunately, few good observations of the lines exist due to their wavelength near 280 nm the ultraviolet. However, a fair number of observations (on the order of 200) are available from the data base of the UltraViolet Polarimeter and Spectrometer (UVSP) instrument that flew on board of NASA's Solar Maximum Mission (SMM) satellite. In addition, this data base contains a number of spectra that include the Mg I resonance line at (lambda)285.2nm, just longward of the h&k lines. The neutral magnesium line is not as strong as its ionic counterparts and samples slightly lower parts of the atmosphere. Its width is a sensitive diagnostic of the ionization balance between neutral and singly ionized magnesium, which determines the opacity scale (and formation height) of other diagnostically important MgI lines like the 457.1 nm intercombination line, the magnesium b lines and the infrared MgI emission lines near 12 microns. Analysis of the observed line profiles shows that it is necessary to include the effects of partial frequency redistribution (PRD) in the formation of the line as in the case of the h&k lines. This implies that the core of the line is very sensitive to the way scattering is treated in the modeling of the line, and in turn this allows us to separate the uncertain effects in the atomic data (viz. the Van der Waals broadening) from the uncertainties in the underlying atmospheric model. The main objective of this research was to compare observed spectra of the magnesium resonance lines against theoretical line profiles calculated from recent models of the solar atmosphere by Fontenla et al., hereafter called FAL. These models extend earlier solar models by Avrett et al. and provide yet a better match between observed and calculated spectra, in particular of the hydrogen Lyman line, by including the effects of ambipolar diffusion of hydrogen and helium in the mass and energy transport equations for the chromosphere-corona transition region. Although the transition region models can be built self-consistently (without additional observational input) once the proper boundary conditions are given at the top of the chromosphere, there are uncertainties in the models precisely because these boundary conditions are not well known. With the analysis of UVSP magnesium observations we strive to constrain these uncertainties.
Avrett, Eugene H.↗
Cross-effects in microgravity flows
In microgravity materials growth (i.e., crystal growth via vapor deposition) experiments, it is of interest ot understand and control the flows that arise from the molecular rather than the mere continuum nature of the gases and the vapors. The project research is a theoretical and experimental investigation of the flow of gas/vapor mixtures in realistic geometries and environments, as well as the application of new fundamental understandings to simulating flows in the ampoules. Towards this goal, the research tasks are: to obtain a theoretical description of the flow by solving appropriate kinetics equations; to verify the results by acquiring experimental data in a diffusion cell; and to explore applications of the results above to simulations of flows in the ampoules. The paper provides a description of the cross-phenomena and the progress realized to-date by the project personnel.
Loyalka, Sudarshan K.↗
Stochastic Optimal Control via Bellman's Principle
This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.
Crespo, Luis G.↗
Badhwar-O'Neill 2014 Galactic Cosmic Ray Flux Model Description
The Badhwar-O'Neill (BON) Galactic Cosmic Ray (GCR) model is based on GCR measurements from particle detectors. The model has mainly been used by NASA to certify microelectronic systems and the analysis of radiation health risks to astronauts in space missions. The BON14 model numerically solves the Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration under the assumption of a spherically symmetric heliosphere. The model also incorporates an empirical time delay function to account for the lag of the solar activity to reach the boundary of the heliosphere. This technical paper describes the most recent improvements in parameter fits to the BON model (BON14). Using a comprehensive measurement database, it is shown that BON14 is significantly improved over the previous version, BON11.
O'Neill, P. M.↗
NASA Galactic Cosmic Radiation Environment Model: Badhwar-O'Neill (2014)
The Badhwar‐O'Neill (BON) Galactic Cosmic Ray (GCR) flux model is used by NASA to certify microelectronic systems and in the analysis of radiation health risks for human space flight missions. Of special interest to NASA is the kinetic energy region below 4.0 GeV/n due to the fact that exposure from GCR behind shielding (e.g., inside a space vehicle) is heavily influenced by the GCR particles from this energy domain. The BON model numerically solves the Fokker‐Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration under the assumption of a spherically symmetric heliosphere. The model utilizes a GCR measurements database from various particle detectors to determine the boundary conditions. By using an updated GCR database and improved model fit parameters, the new BON model (BON14) is significantly improved over the previous BON models for describing the GCR radiation environment of interest to human space flight.
O'Neill, P. M.↗