Role of charge separation and pressure diffusion in the gascap of entry objects
Diffusive transport term in hydrodynamic equations describing flow over strongly ablating entry objects, discussing charge separation and pressure diffusion
Howe, J. T.↗
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Diffusion and viscosity coefficients for helium
The first order Boltzmann-Fokker-Planck equation is solved numerically to obtain diffusion and viscosity coefficients for a ternary gas mixture composed of electron, protons, and helium. The coefficients are tabulated for five He/H abundances ranging from 0.01 to 10 and for both He II and He III. Comparison with Burgers's thermal diffusion coefficients reveals a maximum difference of 9-10% for both He II and He III throughout the range of helium abundances considered. The viscosity coefficients are compared to those of Chapman and Cowling and show a maximum difference of only 5-6% for He II but 15-16% for He III. For the astrophysically important gas mixtures, it is concluded that the results of existing studies which employed Burgers's or Chapman and Cowling's coefficients will remain substantially unaltered.
Roussel-Dupre, R.↗
Cosmic-ray transport in accelerating flows
The quasi-linear transport equation of energetic charged particles is derived, including scattering by Alfven waves propagating parallel and antiparallel to a uniform magnetic field, losses by synchrotron radiation, and acceleration of the cold background fluid supporting the waves. As in the comoving frame equations of radiative transfer, scattering, and loss terms are evaluated in the frame in which the fluid is locally at rest. The diffusion approximation is applied to the resulting equation, yielding a transport equation for the isotropic part of the distribution function and a first-order approximation to the anisotropy. The conditions under which this approximation may be applied are discussed. In the nonrelativistic regime, the standard equation of the diffusion approximation is recovered. As contributions previously investigated, new effects appear from the spatial and temporal variations of the fluid velocity as well as the synchrotron radiation terms. These are discussed in detail.
Kirk, John G.↗
Nonstationary radiation field
Radiation diffusion without redistribution by frequencies, equations for radiative transfer, and stellar spectrum
DIFFUSION WAVE↗
An analysis of the flow field near the fuel injection location in a gas core reactor.
An analytical study is presented which shows the effects of large energy release and the concurrent high acceleration of inner stream fluid on the coaxial flow field in a gas core reactor. The governing equations include the assumptions of only radial radiative transport of energy represented as an energy diffusion term in the Euler equations. The method of integral relations is used to obtain the numerical solution. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.
Weinstein, H.↗
Numerical solution of the radiation transport equation in disk geometry
An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.
Spagna, George F., Jr.↗
Computing diffuse reflection from particulate planetary surface with a new function
An equation is derived to compute the amount of diffuse light reflected by a particulate surface, such as on Mars or an asteroid. The method traces the paths of rays within an ensemble of randomly shaped grains and finds the eventual probability of emission. The amount of diffuse, unpolarized emitted light is obtained in terms of the real index of refraction, the imaginary index, and the average diameter of particles making up the surface. The equation is used to compute the empirical rule for obtaining the planetary albedo from the slope of its polarization curve. Accuracy of the equation, estimated at + or - 4%, seems justified because of quantitative agreement with experimental measures of the empirical rule. It is also shown that the equation can be applied to bubble-enclosing surfaces such as volcanic foams. Results for the indices of the moon, Mars, Io, and Europa are obtained and compared with other data.
Wolff, M.↗
What Would a Dynamo Theorist like to Know About the Dynamics of the Solar Convection Zone?
Observations about the current status of solar dynamo theory are given. The induction equation for magnetic field is solved using assumed velocities and parametric representations of the inductive or diffusive effects of velocities. The equations of motion governing these flow are not solved in parallel. Results from global compressible convection models are discussed. Differential rotation and convection are also investigated.
Gilman, P. A.↗
Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics
The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.
Wood, William A.↗
Heat transfer, diffusion, and evaporation
Although it has long been known that the differential equations of the heat-transfer and diffusion processes are identical, application to technical problems has only recently been made. In 1916 it was shown that the speed of oxidation of the carbon in iron ore depends upon the speed with which the oxygen of the combustion air diffuses through the core of gas surrounding the carbon surface. The identity previously referred to was then used to calculate the amount of oxygen diffusing to the carbon surface on the basis of the heat transfer between the gas stream and the carbon surface. Then in 1921, H. Thoma reversed that procedure; he used diffusion experiments to determine heat-transfer coefficients. Recently Lohrisch has extended this work by experiment. A technically very important application of the identity of heat transfer and diffusion is that of the cooling tower, since in this case both processes occur simultaneously.
GASES - DIFFUSION↗
The prediction of nozzle performance and heat transfer in hydrogen/oxygen rocket engines with transpiration cooling, film cooling, and high area ratios
An advanced engineering computational model has been developed to aid in the analysis and design of hydrogen/oxygen chemical rocket engines. The complete multi-species, chemically reacting and diffusing Navier-Stokes equations are modelled, finite difference approach that is tailored to be conservative in an axisymmetric coordinate system for both the inviscid and viscous terms. Demonstration cases are presented for a 1030:1 area ratio nozzle, a 25 lbf film cooled nozzle, and transpiration cooled plug-and-spool rocket engine. The results indicate that the thrust coefficient predictions of the 1030:1 nozzle and the film cooled nozzle are within 0.2 to 0.5 percent, respectively, of experimental measurements when all of the chemical reaction and diffusion terms are considered. Further, the model's predictions agree very well with the heat transfer measurements made in all of the nozzle test cases. The Soret thermal diffusion term is demonstrated to have a significant effect on the predicted mass fraction of hydrogen along the wall of the nozzle in both the laminar flow 1030:1 nozzle and the turbulent plug-and-spool rocket engine analysis cases performed. Further, the Soret term was shown to represent a significant fraction of the diffusion fluxes occurring in the transpiration cooled rocket engine.
Kacynski, Kenneth J.↗
Influence of the interplanetary magnetic field on cometary and primordial dust orbits - Applications of Lorentz Scattering
The equations describing the change in orbital elements of interplanetary dust due to Lorentz-force accelerations are presented in a simplified form. Such accelerations depend on the charge state of the dust; results of theoretical calculations for five possible dust materials are presented. Under present-day conditions, it is possible that semiconducting material such as graphite might carry a net voltage near zero, compared with a roughly 10-V charge expected for other grains. The scattering of dust by a randomly changing magnetic field can be viewed analogously to the dust diffusing in space; the equations presented thus can be used to interpret observations of the present distribution of dust in terms of its possible sources and sinks. The stronger magnetic fields of the early solar system would have led to more vigorous scattering of the dust; particles as large as 1 mm could have been significantly transported by Lorentz scattering during this time.
Consolmagno, G. J.↗
An asymptotic description of transient settling and ultrafiltration of colloidal dispersions
The present model for the sedimentation of colloidal systems includes a diffusion term in the governing equation which, in the regions above the sediment, acts as small perturbation to the Kynch (1952) theory. Within the sediment, diffusion is comparable to convection due to the the high solid volume fraction. An application of the method of matched asymptotic expansions to the conservation equation allows a complete description of the settling process to be formulated, with specific attention to volume-fraction evolution in the sediment.
Davis, K. E.↗
Remobilizing the Interfaces of Thermocapillary Driven Bubbles Retarded by the Adsorption of a Surfactant Impurity on the Bubble Surface
Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is applied to the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow which propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillarity to direct the movement of bubbles in space is the fact that surfactant impurities which are unavoidably present in the continuous phase can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature tension gradient, and decreases to near zero the thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have been retarded by the adsorption onto the bubble surface of a surfactant impurity, Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition the rapid kinetic exchange and high bulk concentration maintain a saturated surface with a uniform surface concentrations. This prevents retarding surface tension gradients and keeps the velocity high. In our first report last year, we detailed experimental results which verified the theory of remobilization in ground based experiments in which the steady velocity of rising bubbles was measured in a continuous phase consisting of a glycerol/water mixture containing a polyethylene glycol surfactant C12E6 (CH3(CH2)11(OCH2CH2)6OH). In our report this year, we detail our efforts to describe theoretically the remobilization observed. We construct a model in which a bubble rises steadily by buoyancy in a continuous (Newtonian) viscous fluid containing surfactant with a uniform far field bulk concentration. We account for the effects of inertia as well as viscosity in the flow in the continuous phase caused by the bubble motion (order one Reynolds number), and we assume that the bubble shape remains spherical (viscous and inertial forces are smaller than capillary forces, i e. small Weber and capillary numbers). The surfactant distribution is calculated by solving the mass transfer equations including convection and diffusion in the bulk, and finite kinetic exchange the bulk and the surface. Convective effects dominate diffusive mass transfer in the bulk of the liquid (high Peclet numbers) except in a thin boundary layer near the surface. A finite volume method is used to numerically solve the hydrodynamic and mass transfer equations on a staggered grid which accounts specifically for the thin boundary layer. We present the results of the nondimensional drag as a function of the bulk concentration of surfactant for different rates of kinetic exchange, from which we develop criteria for the concentration necessary to develop a prescribed degree of remobilization. The criteria compare favorably with the experimental results.
Palaparthi, Ravi↗
An equation for the local thermal emissivity at the vertex of a diffuse conical or V-groove cavity.
Local emissivity of vertex point of diffuse conical or V-groove cavity, noting dependence on wall material, angle factor and agreement with theoretical solution
INTEGRAL EQUATION↗
Inward radial diffusion of electrons e greater than 1.6 mev in the outer radiation zone
Energetic electron intensities radial flow diffusion in outer radiation belt near geomagnetic equator
ELECTRON INTENSITY↗
Dynamic response of shock waves in transonic diffuser and supersonic inlet - An analysis with the Navier-Stokes equations and adaptive grid
An existing method which solves the multi-dimensional ensemble-averaged compressible time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique has been extended to include the shock-tracking adaptive grid systems. The numerical scheme for solving the governing equations is based on a linearized block implicit approach. The effects of grid-motion and grid-distribution on the calculated flow solutions have been studied in relative detail and this is carried out in the context of physically steady, shocked flows computed with non-stationary grids. Subsequently, the unsteady dynamics of the flows occurring in a supercritically operated transonic diffuser and a mixed compression supersonic inlet have been investigated with the adaptive grid systems by solving the Navier-Stokes equations.
Liu, N.-S.↗
Chemical potential effects on neutrino diffusion in supernovae
The validity of imposing a zero chemical potential for neutrinos in hydrodynamic calculations of collapsing supernovae is investigated in the diffusion approximation of neutrino transport. A coupled system of equations is solved for neutrino and energy diffusion fluxes as well as lepton diffusion in a collapsing supernovae ambient medium, and the results indicate a substantial growth in the neutrino chemical potential for densities greater than 10 to the 12th power gm/cu cm. The rate of energy transport is shown to be significantly affected by increases in Fermi integrals and chemical-potential gradients accompanied by decreases in temperature, and the extent of neutrino particle/antiparticle reactions is found also to affect energy diffusion rates. It is concluded that the photon-like behavior usually assumed for neutrinos may be incorrect and that an extension of the Sn transport approximation to include lepton characteristics is necessary for a definitive answer to the question of neutrino transport in supernovae.
Mazurek, T. J.↗