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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 181 records · Page 10
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NASA NTRS1977

On the hydrodynamic expansion of a relativistic gas

An exact solution to the one-dimensional relativistic Euler equations is presented which is not of a self-similar nature and which satisfies certain initial conditions found to be appropriate in describing high-energy cosmic-ray collisions and models of radio galaxies. A full numerical analysis is performed to demonstrate the temporal behavior of all relevant thermodynamic quantities at any given point in the expansion. The results indicate that the motion is self-similar at the very beginning of free expansion, that this description ceases to be valid when the entire bulk of fluid is in motion, and that with the passage of time, the nonsimilar solution prevails over more and more of the fluid except for a small region near the leading edge where the fluid borders on the vacuum. The very bulk of the expansion is shown to become nonsimilar because the leading edge of the self-similar solution moves into the vacuum at the speed of light while that of the nonsimilar solution approaches c only asymptotically. The relativistic expansion of a gaseous disk is analyzed as an example.

Canuto, V.↗
NASA NTRS1977

Renal sodium reabsorption following induction of and recovery from volume expansion

In the rat, infusion of a volume of isotonic saline equal to 2% of body weight resulted in an 82% increase in the delivery of filtrate out of the proximal tubule but little or, in some animals, no change in the urinary excretion of sodium. By contrast, further degrees of volume expansion resulted in lesser increases in the distal delivery of filtrate, but were associated with a marked increase in the urinary excretion of sodium. Sixty minutes following completion of volume expansion, while the animals were still in positive sodium balance, the urinary excretion of sodium decreased 52% compared to a decrease of only 24% in the distal delivery of filtrate. During the course of progressive volume expansion and during the recovery phase, there was a dissociation between alterations in sodium reabsorption in the proximal convoluted tubule and in the whole kidney. These studies indicate that although the proximal tubule is more sensitive to changes in the extracellular fluid volume, distal nephron sites are ultimately responsible both for the natriuresis of volume expansion and the relative antinatriuresis of the recovery periods.

Knight, T. F.↗
NASA NTRS1978

A strictly Markovian expansion for plasma turbulence theory

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest non-trivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.

Jones, F. C.↗
NASA NTRS1980

Errors incurred in a plane-wave-type expansion of a Gaussian beam

The multipole expansion obtained by Morita et al. (1968) of the Gaussian laser beam used to levitate an aerosol particle in order that its complete phase matrix may be measured is compared with that of Tsai and Pogorzelski (1975) in order to demonstrate the effect of the incorrect expansion used by Morita. Errors incurred by the use of an equation in which one side satisfies the scalar wave equation while the other side does not and can be reduced to a plane wave amplitude are calculated as functions of the inverse of the wave number times the beam waist, the wave number times the radial spherical coordinate and the angular spherical coordinate. Errors on the order of a few percent, considered undetectable are obtained in the squared-field amplitudes due to the expansion, however, they are found to become significant (several tens of percent) when the angle is zero. It is concluded that the expansion of Morita should only be used in the regions where the spherical angle is less than 0.01 and its product with the wave number and the radial spherical coordinate is less than unity.

Kattawar, G. W.↗
NASA NTRS1982

Power series expansions for the frequency and period of the limit cycle of the van der Pol equation

An equation reported by van der Pol (1926) in connection with relaxation-oscillations studies is considered. The equation contains the factor epsilon which can assume values in the range from zero to infinity. The period T(epsilon), or equivalently the frequency nu(epsilon) of the limit cycle has been studied. However, to date there has been little success in discovering the analytical structure of T(epsilon) as a function of epsilon. The present investigation has the objectives to present the Taylor series expansion of nu(epsilon), to locate the singularities which determine the radius of convergence of that expansion, to introduce a new damping variable in terms of which the expansion converges for all epsilon, to form a new expansion for the period T(epsilon) which improves the rate of convergence of the series, to attempt to 'complete' the series, and to compare the obtained results with the numerically determined values of T(epsilon) and with the asymptotic approximation valid for large epsilon.

Andersen, C. M.↗
NASA NTRS1982

Numerical calculations relevant to the initial expansion of the polar wind

The results of a numerical simulation of the expansion of an H(+)-0(+) electron plasma into a vacuum are reported. Variations were introduced in the ionic density ratios, the scale lengths for the density gradient at the plasma-vacuum interface, and the initial electron-ion temperature ratio. Conditions of a gravitationally bound O(+) plasma were also considered. It was found that if H(+) is a major ion, the H(+) density profile in the expansion region is always concave, with a phase-space divided into three regions, i.e., an undisturbed plasma, a rarefaction region, and an expansion region in which ions are accelerated. When the H(+) is a minor ion, the O(+) ions accelerate the H(+) ions, the H(+) phase-space is divided into five regions, and the increased electron temperatures produce enhanced electrostatic potentials and H(+) drifts in the expansion region.

Singh, N.↗
NASA NTRS1984

Electron radiation effects on the thermal expansion of graphite/resin composites

The effects of 1 MeV electron radiation on the thermal expansion characteristics of two graphite reinforced resin matrix composite systems were studied. Specimens of both graphite/epoxy (T300/5208) and graphite/polyimide (C6000/PMR15) were irradiated to a total dose of 6 x 10 to the 9th rads at two different rates. Dynamic mechanical analyses (DMA) were performed to study changes in resin chemistry. Thermal expansion results indicate that radiation did produce permanent residual strains of up to -70 x 10 to the -6th for the graphite/epoxy when exposed to temperatures up to +280 F. However, no permaanent changes in the coefficient of thermal expansion (CTE) were observed. No permanent residual strains or changes in the CTE attributable to radiation were observed for the graphite/polyimide specimens. DMA results indicate that electron radiation caused chemical changes in the epoxy matrix. These changes resulted in a lower glass transition temperature and broader 'rubbery region' which extended into the temperature range of the thermal expansion tests.

Bowles, D. E.↗
NASA NTRS1986

Studies on counterstreaming plasma expansion

Recent studies on counterstreaming plasma expansions are summarized. The basic phenomenon of plasma expansion is reviewed, and results from one-dimensional simulations of counterstreaming plasma expansion are discussed. Results from simulations based on an electrostatic particle-in-cell code, in which the dynamics of both the electrons and ions are exactly followed, are discussed. The formation of electrostatic shocks is addressed. Finally, results are presented on the ionospheric plasma expansion along the geomagnetic flux tubes by solving the hydrodynamic equations.

Singh, N.↗
NASA NTRS1986

More on the expansion of a collisionless plasma into the wake of a body

Recent laboratory measurements of plasma expansion in a plasma wake experiment (Wright et al., 1985) are compared with analytical expressions which approximate the plasma expansion model of Crow et al. (1975). Good quantitative agreement is found between the data and theory for the velocity and position of the ion expansion front. These results provide an important insight into the behavior of the expansion early in its development.

Wright, K. H., Jr.↗
NASA NTRS1988

Karhunen-Loeve expansion of Burgers' model of turbulence

The properties of the Karhunen-Loeve expansion of a strongly inhomogeneous random process are examined with emphasis on applications to turbulent flow fields. The ability of the KL expansion to represent functions that have both slow and rapid variations in a relatively small number of expansion terms is tested on a one-dimensional model based on the forced Burgers' equation. The rate of the convergence of the expansion is evaluated, and its dependence on the Reynolds number is determined. It is shown that the KL eigenfunctions possess wall boundary layers attached to outer structures that are independent of the Reynolds number (at high Reynolds numbers). It is also shown that the spectrum of eigenvalues is broad at large Reynolds numbers, requiring many terms to represent higher-order derivatives of the function.

Chambers, D. H.↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1990

Solar wind proton velocity distributions - Comparison of the bi-Maxwellian based 16-moment expansion with observations

The purpose of this paper is to study the possible types of velocity distributions that can be obtained from the bi-Maxwellian based 16-moment expansion of the distribution function, assuming macroscopic parameter values characteristic of the range of solar wind conditions. While previous studies also took heat flow into account, the theoretical expansions for f and the definitions of the physical moments adopted in these studies were different from those used in this paper. The choice of the 16-moment expansion and corresponding moment definitions was motivated by the fact that this is the correct generalization of the widely-used Maxwellian-based 13-moment expansion to the case where the zeroth-order distribution is a bi-Maxwellian. It is found that most of the features characteristic of solar wind proton distributions can be reproduced with the 16-moment distribution, including the appearance of secondary peaks. It is also shown how each of the physically significant velocity moments affects the shape of the distribution function.

Demars, H. G.↗
NASA NTRS1991

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1991

The effect on an acoustic wave as it traverses an unsteady expansion

The shift in fundamental frequency that occurs in acoustic waves is obtained for waves traversing an unsteady expansion. It is shown analytically that downstream of the unsteady expansion all frequencies approach one of an infinite number of discrete frequencies independent of the frequency upstream of the unsteady expansion. This theoretical analysis is used to accurately predict the period of noise observed in an expansion tube when operated at low enthalpies.

Paull, A.↗
NASA NTRS1991

High enthalpy, hypervelocity flows of air and argon in an expansion tube

An expansion tube with a free piston driver has been used to generate quasi-steady hypersonic flows in argon and air at flow velocities in excess of 9 km/s. Irregular test flow unsteadiness has limited the performance of previous expansion tubes, and it has been found that this can be avoided by attention to the interaction between the test gas accelerating expansion and the contact surface in the primary shock tube. Test section measurements of pitot pressure, static pressure and flat plate heat transfer are reported. An approximate analytical theory has been developed for predicting the velocities achieved in the unsteady expansion of the ionizing or dissociating test gas.

Neely, A. J↗
NASA NTRS1992

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1992

Comparison of the Unified Perturbation Method with the two-scale expansion

The Unified Perturbation Method (UPM) converges faster over a wider domain of surface roughness than other perturbations, such as the small perturbation method, the phase perturbation method, the Kirchhoff approximation, and the momentum transfer expansion. It can be shown that UPM intrinsically possess characteristics similar to the two-scale expansion without requiring a free parameter. This paper considers whether the UPM can be improved by applying the two-scale concept to the method. In order to do so, the unknown source current is expanded in a two-scale manner starting from the extinction theorem. Several two-scale expansions are derived and are compared with the conventional two-scale approximation. It is shown that the UPM performs best without two-scale expansions.

Kim, Yunjin↗