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Results for “dispersive equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

The cosmic-ray shock structure problem for relativistic shocks

The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.

Webb, G. M.↗
NASA NTRS1989

The oblique behavior of low-frequency electromagnetic waves excited by newborn cometary ions

The free energy in oxygen or hydrogen ions freshly created in the solar wind stimulates low-frequency electromagnetic waves whose growth does not always maximize at parallel propagation. Exploration of the wave vector plane discloses the frequent occurrence of islets of oblique growth unconnected to the unstable parallel modes. Contour plots of the growth rate, real frequency, polarization, and magnetic compression characterize the oblique wave behavior for large values of the initial pitch angle of the cometary particles. Although wave-particle (Landau and cyclotron) resonances feed most of the surveyed oblique instabilities, some are seemingly fluidlike. The results, obtained from the numerical solution of the kinetic dispersion and wave equations, imply that newborn ions can easily excite significant oblique hydromagnetic wave activity. Cometary environments provide the adopted plasma model, but the study is helpful in the interpretation of other low-frequency wave observations in space.

Brinca, Armando L.↗
NASA NTRS1992

Dispersion-relation-preserving schemes for computational aeroacoustics

Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.

Tam, Christopher K. W.↗
NASA NTRS1978

Approximate line shapes for hydrogen

Two independent methods are presented for calculating radiative transport within hydrogen lines. In Method 1, a simple equation is proposed for calculating the line shape. In Method 2, the line shape is assumed to be a dispersion profile and an equation is presented for calculating the half half-width. The results obtained for the line shapes and curves of growth by the two approximate methods are compared with similar results using the detailed line shapes by Vidal et al.

Sutton, K.↗
NASA NTRS1992

Application of radiative image transfer theory to the assessment of the overall OTF and contrast degradation of an image in an inhomogeneous turbulent and turbid atmosphere

A perturbation-theoretic approximation of the radiative transfer equation which neglects photon dispersion is used as a modeling basis for the propagation of the image of a self-luminous target through a turbulent atmosphere which also possesses inhomogeneously distributed turbidity along the propagation path. A contrast ratio is then introduced which provides an indicator of the relative contribution of the unscattered or coherent image component to that of the scattered or incoherent image component. Analytical expressions are then derived for the contrast ratio from the approximate form of the radiative transfer equation in the case of an inhomogeneously dispersed Joss thunderstorm rain distribution in the presence of turbulence. The case is clearly demonstrated for the need to consider a measure of the points of demarcation at which the dominant roles of the scattering processes due to turbidity and turbulence are exchanged. Such a measure can provide a performance parameter for the application of adaptive optics methods that are specific to the particular dominant scattering mechanism given the prevailing target size, total propagation length and overall propagation parameters.

Manning, Robert M.↗
NASA NTRS1987

Solitary waves in the resonant phenomenon between a surface gravity wave packet and an internal gravity wave

A two-layer inviscid incompressible fluid system of intermediate depth is considered. A multiple-scales perturbation technique is applied to the basic equations and boundary conditions for a two-layer fluid system to derive a system of weakly nonlinear partial integrodifferential equations governing the resonant interaction between a surface gravity wave packet and an internal gravity wave at an intermediate depth, providing a bridge between the existing shallow and deep fluid theories. The convolution integral term in these equations accounts for the dispersion in the lower-layer fluid. An iterative fast Fourier transform scheme is developed to find solitary wave solutions to this system of equations. The overtaking collision of two pairs of solitary waves, simulated using a spectral method, is found to be inelastic. It is found that the amplitude of the solitary waves changes slightly after the collision. The phase shifts these solitary waves undergo was calculated numerically.

Sepulveda, Nicasio↗
NASA NTRS1999

Phenomenological Theory of the Translational Relaxation Times in Gases

The exact solution to the classical equations governing the translational dispersion and absorption of sound in a gas obscures its relaxational character because of its mathematical complexity. The approach taken here is to solve the secular equation by the method of Pade approximants, which even to the relatively low order R(sub 11) yields a remarkably close approximation to the exact solution over a wide range of frequency/pressure (f/P) ratios. As a result, translational relaxation can be formulated in terms of a conventional relaxation process with well-defined relaxation times, relaxation strength, collision numbers, additivity relations, etc. To extend the theory to high values of f/P ratio, a model is proposed to account for the noncontinuum behavior of the transport coefficients (viscosity and thermal conductivity) as the molecular mean free path approaches the acoustical enclosure dimensions. The theoretical dispersion and absorption show good agreement with measurements in argon over the classical and transition regions of f/P, but a discrepancy appears at higher values of f/P, where collective propagating modes, assumed in the theory, give way to single-particle modes, prevailing in the experiments.

Zuckerwar, Allan J.↗
NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗
NASA NTRS1994

Particle Distribution in Suspension Shear Flow

An earlier proposed constitutive relation for normal stresses originated by random particle fluctuations is used to describe a joint effect of thermal and shear-induced fluctuations on concentrational distributions in suspension flow. Averaged products of components of the fluctuation velocity are evaluated on a basis of the rational mechanics approach combined with a simple kinematic consideration. The equation of momentum conservation of the dispersed phase of a suspension closed with this constitutive relation is applied to unidirectional shear flow in the gravity field and to rotational Couette flow. Coupling of the thermal and shear-induced fluctuations results in that the ability of shear flow to suspend particles has a minimum at a certain particle size, all other things being equal. The developed model provides also for a reasonable explanation of particle distributions observed in Couette flow. The approach based on the consideration of momentum balance for the dispersed phase is proved to lead to an effective equation of convective diffusion of the suspended particles. Coefficients of mutual diffusion due to both thermal and shear-induced fluctuations are drastically different from corresponding self-diffusivities as regards both their scaling and their concentrational dependence.

Buyevich, Yu A.↗
NASA NTRS1991

A computer code for multiphase all-speed transient flows in complex geometries. MAST version 1.0

The operation of the MAST code, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the Eulerian-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a Lagrangian tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present code adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present code.

Chen, C. P.↗
NASA NTRS1982

A model study of Fuego volcanic aerosol dispersion in the lower stratosphere

A zonally averaged time-dependent primitive equation model is used to simulate the dispersion of both a carbon 14 injection and the volcanic aerosol from the 1974 Fuego eruption. It is noted that both injections occurred at low latitudes to midlatitudes in the Northern Hemisphere. The eddy flux terms, which account for the major portion of the transport in the lower stratosphere of this model, are specified in a manner similar to that of Harwood and Pyle (1975). Comparisons with data underline the ability of the model to simulate the vertical character of the tracer while maintaining reasonable meridional transport times. For the aerosol study, the simulated 1/e decay time at 37 deg N and for the 16- to 21-km altitude region is 9 months, whereas lidar measurements at the same latitude give a decay time of 8 months. The simulated vertical width at half-maximum for the aerosol tracer at 37 deg N and 19 deg N and for 6 months after the event possesses values of 5.0 km and 3.6 km, respectively, whereas the observed lidar values are 4.4 km and 3.0 km, respectively. The tracer transport to the Southern Hemisphere also is in qualitative agreement with the limited data that are available.

Remsberg, E. E.↗
NASA NTRS1983

Analysis of the error associated with grid representation of point sources

The steady-state, three-dimensional transport equation for inert pollutant dispersion in the atmosphere is solved analytically to obtain expressions for pollutant concentrations from both a point source and a rectangular area source. The results of this analysis have application to numerical grid models in which the smallest resolvable source is the size of a single grid. The concentrations at ground level along the plume centerline from the two types of sources are in close agreement with each other at distances greater than 10 km downwind when the horizontal dimension of the rectangular source is not less than 100 m. The dimension of the source in the vertical direction is held constant at 50 m. Similar results are obtained for concentrations along the plume centerline at the effective stack height. When the size of the source in the crosswind direction is increased to 1 km, good agreement between the two concentrations is obtained for downwind distances over 60 km for the ground level case and over 140 km for the concentration at stack height level. For the horizontal dimension equal to 10 km, good agreement between the two cases is only obtained at extremely large downwind distances at both the stack height and ground levels.

Karamchandani, P.↗
NASA NTRS1991

Scalar dissipation and mixing in turbulent reacting flows

The mixing term that appears in probability density function-based formulations of the statistical behavior of turbulent reacting flows was studied with the use of direct numerical simulations of an irreversible, second-order, isothermal chemical reaction between initially segregated reactants in decaying, homogeneous turbulence. Three-dimensional, time-dependent pseudospectral calculations with 64-cubed Fourier modes were made as well as were Monte Carlo simulations of the joint concentration pdf equations for coalescence-dispersion (C/D) models. It was found that the development of the scalar microscales depends largely on the initial concentration distributions (both isotropic and nonisotropic distributions were used) and is relatively independent of the reaction rate constant. Joint concentration probability density functions were compared to predictions of D/D models that make use of parameters evaluated from the nonreacting or inert system.

Leonard, Andy D.↗
NASA NTRS1993

Modelling of dispersal and deposition of impact glass spherules from the Cretaceous-Tertiary boundary deposit

The dispersal of glass spherules or tektites from a bolide impact with the Earth is modelled as ballistic trajectories in standard atmosphere. Ballistic dispersal of Cretaceous-Tertiary boundary impact glass spherules found in Haiti and Mimbral, Mexico requires a fireball radius in excess of 50 km but less than 100 km to account for the observed distribution. Glass spherules from 1 and up to 8 mm in diameter have been found at the KT boundary at Beloc in Haiti, at Mimbral, Mexico, and at DSDP Sites 536 and 540 in the Gulf of Mexico corresponding to paleodistances of 600 to 1000 km from the Chicxulub crater. In Haiti the basal and major glass-bearing unit at the KT boundary is attributed to fallout on basis of sedimentologic features. When compared with theoretical and observed dispersal of volcanic ejecta, the grain size versus distance relationship of the KT boundary tektite fallout is extreme, and rules out a volcanic fallout origin. At a comparable distance from source, the KT impact glass spherules are more than an order of mangitude coarser than ejecta of the largest known volcanic events. We model the dispersal of KT boundary impact glass spherules as ballistic ejecta from a fireball generated by the impact of a 10 km diameter bolide. Mass of ejecta in the fireball is taken as twice the bolide mass. Melt droplets are accelerated by gas flow in the fireball cloud, and leave the fireball on ballistic trajectories within the atmosphere, subject to drag, depending on angle of ejection and altitude. The model for ballistic dispersal is based on equations of motion, drag and ablation for silicate spheres in standard atmosphere.

Espindola, J. M.↗