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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Energetic particle transport in relativistic flows

A discussion is given of pitch angle dependent and diffusive transport equations for cosmic rays applicable for both special relativistic and general relativistic flows, derived from the relativistic Boltzmann equation. As an example of particle transport in a curved spacetime we give a pitch angle dependent transport equation appropriate for radial accretion onto a Schwarzschild black hole. The roles of fluid shear, acceleration and compression on the energy changes of particles in the diffusive transport equations are emphasized. Also discussed are special flows (e.g. rigidly rotating flows) associated with a Killing vector for which a constant of the motion of the particles can be identified, and for which simplified transport equations can be constructed.

Webb, G. M.↗
NASA NTRS1985

Momentum-dependent diffusive particle acceleration in modified shock fronts

In the presently derived analytic solutions of the steady transport equation for diffusive particle acceleration in a modified, planar shock front having free escape boundaries, the fluid velocity profile through the shock transition decreases monotonically between the upstream and downstream boundaries. The spatial diffusion coefficient's spatial dependence is linked to that of the fluid velocity profile. Attention is given to the solution corresponding to monoenergetic particle injection at the shock front, with free particle escape at finite distances both upstream and downstream of the shock. The accelerated particle spectrum is dominated at high energies by an exponential cutoff, due to the competition between acceleration by the first-order Fermi mechanism and particle loss through the free escape boundaries.

Webb, G. M.↗
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 NTRS1989

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

Ho, Lee-Wing↗
NASA NTRS1977

Some basic mathematical methods of diffusion theory

An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.

Giere, A. C.↗
NASA NTRS1974

Combustion of hydrogen-air jets in local chemical equilibrium: A guide to the CHARNAL computer program

A guide to a computer program, written in FORTRAN 4, for predicting the flow properties of turbulent mixing with combustion of a circular jet of hydrogen into a co-flowing stream of air is presented. The program, which is based upon the Imperial College group's PASSA series, solves differential equations for diffusion and dissipation of turbulent kinetic energy and also of the R.M.S. fluctuation of hydrogen concentration. The effective turbulent viscosity for use in the shear stress equation is computed. Chemical equilibrium is assumed throughout the flow.

Spalding, D. B.↗
NASA NTRSDate not supplied

Finite-Volume Diffusion Schemes for Svard's Eulerian Governing Equations

This paper, contains discussion on the implementation of new diffusion schemes for Svard’s Eulerian flow (EF) governing equations. It contains an alpha-damping type scheme and a new hyperbolic Eulerian flow (HEF) discretization paralleling previous work on hyperbolic Navier-Stokes (HNS). It shows these equations have simplified hyperbolic discretizations due to the simplicity of the new stress tensor and compares these schemes to established Navier-Stokes (NS) discretizations to verify the predictive utilities of such diffusion schemes.

Computational Fluid Dynamics↗
NASA NTRS2024

Finite-Volume Diffusion Schemes for Svard's Eulerian Governing Equations

This paper, contains discussion on the implementation of new diffusion schemes for Svard’s Eulerian flow (EF) governing equations. It contains an alpha-damping type scheme and a new hyperbolic Eulerian flow (HEF) discretization paralleling previous work on hyperbolic Navier-Stokes (HNS). It shows these equations have simplified hyperbolic discretizations due to the simplicity of the new stress tensor and compares these schemes to established Navier-Stokes (NS) discretizations to verify the predictive utilities of such diffusion schemes.

Computational Fluid Dynamics↗
NASA NTRS1984

Direct simulations of chemically reacting turbulent mixing layers

The report presents the results of direct numerical simulations of chemically reacting turbulent mixing layers. The work consists of two parts: (1) the development and testing of a spectral numerical computer code that treats the diffusion reaction equations; and (2) the simulation of a series of cases of chemical reactions occurring on mixing layers. The reaction considered is a binary, irreversible reaction with no heat release. The reacting species are nonpremixed. The results of the numerical tests indicate that the high accuracy of the spectral methods observed for rigid body rotation are also obtained when diffusion, reaction, and more complex flows are considered. In the simulations, the effects of vortex rollup and smaller scale turbulence on the overall reaction rates are investigated. The simulation results are found to be in approximate agreement with similarity theory. Comparisons of simulation results with certain modeling hypotheses indicate limitations in these hypotheses. The nondimensional product thickness computed from the simulations is compared with laboratory values and is found to be in reasonable agreement, especially since there are no adjustable constants in the method.

Riley, J. J.↗
NASA NTRS1978

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

May, C. E.↗
NASA NTRS1978

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

May, C. E.↗
NASA NTRS1992

An analytic model of the neutral cloud evolution in the earth's atmosphere

An analytic model for the expansion of a chemically reacting gas in the upper atmosphere is discussed. The spatial-temporal distribution of released particles in the initial regime is described on the basis of self-similar solutions of Euler's equations. In the case of transition to the diffusion regime an approximate solution of the kinetic equation with the collision integral in the form of BGK is performed. Gravitation and the atmospheric inhomogeneity are taken into account, The diffusion regime is described by an analytic solution of the diffusion equation in an exponential atmosphere taking account of possible losses of the gas due to chemical reactions. Some peculiarities of the expansion of various gases as well as the possibility of applying the model for describing ionospheric 'holes' are discussed.

Bruskin, L. G.↗
NASA NTRS1980

The dynamics of oceanic fronts. I - The Gulf Stream

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Kao, T. W.↗
NASA NTRS1995

Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.

Frank, Adam↗
NASA NTRS2000

Numerical Simulation of a Chemically Reacting Sorbent Bed for LSS Applications

A detailed numerical model of a chemisorption bed has been developed. The model is based on the constant pressure mass transport equation for gaseous flow through a packed bed, and the equation for diffusion and reaction within a spherical particle. Because there is a wealth of data from the NASA and the Navy bodies of literature, the LiOH-H2O-CO2 system is chosen for application of the model and interpretation of results. Prior models of this system from the life support literature are limited. The current model incorporates many of the features of elaborate models developed for investigation of industrial systems or energy applications (e.g., coal, desulphurization): it distinguishes bulk convection and bed dispersion; mass transport to the particle surface, transport within the particle, and reaction. It uses the nonsteady (not pseudo-steady state) form of the equations. The chemistry is modeled as a multi-step, reversible reaction with evolving solid structure. The resulting system of equations is large. The ODEPACK family of solvers is used to integrate the system. Reaction coefficients are determined by experiment. Typical results of the model are illustrated with mission input parameters. Using the model, an explanation is offered for 1) the varied performance results found after pre-breathing (or after simulated pre-breathe conditions), 2) interrupted use and 3) low temperature use. In addition, options for a reusable canister are explored. The computational resource implications of adding energy equations are discussed briefly, as are applicability to other relevant space and undersea systems.

Luna, Bernadette↗
NASA NTRS1993

An alternative model for estimating liquid diffusion coefficients requiring no viscosity data

An equation, based on the free volume of a liquid solvent, was derived via dimensional analysis, to predict binary diffusion coefficients. The equation assumed that interaction between the solute and liquid solvent molecules followed a Lennard-Jones potential. The equation was compared to other diffusivity equations and was found to give good results over the temperature range examined.

Morales, Wilfredo↗