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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics

A new time-dependent neutron transport method based on the method of characteristics (MOC) has been developed. Whereas most spatial kinetics methods treat time dependence through temporal discretization, this new method treats time dependence by defining the characteristics to span space and time. In this implementation regions are defined in space-time where the thickness of the region in time fulfills an analogous role to the time step in discretized methods. The time dependence of the local source is approximated using a truncated Taylor series expansion with high order derivatives approximated using backward differences, permitting the solution of the resulting space-time characteristic equation. To avoid a drastic increase in computational expense and memory requirements due to solving many discrete characteristics in the space-time planes, the temporal variation of the boundary source is similarly approximated. This allows the characteristics in the space-time plane to be represented analytically rather than discretely, resulting in an algorithm comparable in implementation and expense to one that arises from conventional time integration techniques. Furthermore, by defining the boundary flux time derivative in terms of the preceding local source time derivative and boundary flux time derivative, the need to store angularly-dependent data is avoided without approximating the angular dependence of the angular flux time derivative. The accuracy of this method is assessed through implementation in the neutron transport code DeCART. The method is employed with variable-order local source representation to model a TWIGL transient. The results demonstrate that this method is accurate and more efficient than the discretized method. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Size exclusion deep bed filtration: Experimental and modelling uncertainties

A detailed uncertainty analysis associated with carboxyl-modified latex particle capture in glass bead-formed porous media enabled verification of the two theoretical stochastic models for prediction of particle retention due to size exclusion. At the beginning of this analysis it is established that size exclusion is a dominant particle capture mechanism in the present study: calculated significant repulsive Derjaguin-Landau-Verwey-Overbeek potential between latex particles and glass beads is an indication of their mutual repulsion, thus, fulfilling the necessary condition for size exclusion. Applying linear uncertainty propagation method in the form of truncated Taylor's series expansion, combined standard uncertainties (CSUs) in normalised suspended particle concentrations are calculated using CSUs in experimentally determined parameters such as: an inlet volumetric flowrate of suspension, particle number in suspensions, particle concentrations in inlet and outlet streams, particle and pore throat size distributions. Weathering of glass beads in high alkaline solutions does not appreciably change particle size distribution, and, therefore, is not considered as an additional contributor to the weighted mean particle radius and corresponded weighted mean standard deviation. Weighted mean particle radius and LogNormal mean pore throat radius are characterised by the highest CSUs among all experimental parameters translating to high CSU in the jamming ratio factor (dimensionless particle size). Normalised suspended particle concentrations calculated via two theoretical models are characterised by higher CSUs than those for experimental data. The model accounting the fraction of inaccessible flow as a function of latex particle radius excellently predicts normalised suspended particle concentrations for the whole range of jamming ratios. The presented uncertainty analysis can be also used for comparison of intra- and inter-laboratory particle size exclusion data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Application of Simplified Pn Approximation to Angular Distribution of Neutron Source in MOC Calculations

Concept of the simplified Pn approximation is applied to represent angular distribution of anisotropic scattering source in order to decrease number of angular flux moments stored during transport sweeps. In practical design calculations, anisotropic scattering is usually taken into account through transport correction. Though the transport correction yields a reasonable result for many cases, detail treatment of anisotropic scattering is desirable in high fidelity neutronics calculations, e.g., a direct heterogeneous transport calculation in three dimensional geometry. Direct treatment of anisotropic scattering has been established, which commonly utilizes the series expansion by the spherical harmonics functions. The expansion by the spherical harmonics functions requires (L + 1){sup 2} angular flux moments when up to L-th order anisotropy is taken into account. The previous studies suggested that consideration up to P3 anisotropic scattering yields converged results in many neutronics analysis for LWR. In this case, (3 + 1){sup 2} = 16 angular flux moments should be stored and retained in each flux region of each energy group. This storage requirement would be significant in a large scale calculation with many flux regions and energy groups. Chao et al. proposed an explicit angular flux representation based on the simplified Pn (SPn) method. Number of angular flux moments required in a SPn calculation is (L + 1) when L-th order angular distribution is considered. Since the SPn method adopts the physical picture of 'locally 1D system' along particular direction, required number of angular flux moments is much smaller than that based on the spherical harmonics functions. In the present study, concept of the SPn method is applied to describe angular distribution of anisotropic scattering source. By adopting the SPn approximation, as described above, number of angular flux moments can be significantly reduced. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Annular spherically focused ring transducers for improved single-beam acoustical tweezers

The use of ultrasonic transducers with a central hollow is suggested for improved single-beam acoustical tweezers applications. Within the framework of the Fresnel-Kirchhoff parabolic approximation, a closed-form partial-wave series expansion (PWSE) for the incident velocity potential (or pressure) field is derived for an annular spherically focused ring (asfr) with uniform vibration across its surface in spherical coordinates. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSE assuming a weakly focused beam (with a focusing angle α ≤ 20°). The PWSE allows evaluating the incident field from the finite asfr in 3D. Moreover, the obtained solution allows computing efficiently the acoustic scattering and radiation force on a sphere centered on the beam's axis of wave propagation. The analytical solution is valid for wavelengths largely exceeding the radius of the asfr and when the viscosity of the surrounding fluid can be neglected. Numerical predictions for the beam-forming, scattering, and axial time-averaged radiation force are performed with particular emphasis on the asfr thickness, the axial distance separating the sphere from the center of the transducer, the (non-dimensional) size of the transducer, as well as the sphere's elastic properties without restriction to the long- (i.e., Rayleigh) or the short-wavelength (i.e., ray acoustics) regimes. Potential applications of the present solution are in beam-forming design, particle tweezing, and manipulation due to negative forces using ultrasonic asfr transducers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence

This paper presents two key contributions; the first concerns the development of analytical expressions for the axial and transverse acoustic radiation forces exerted on a 2D rigid elliptical cylinder placed in the field of plane progressive, quasi-standing, or standing waves with arbitrary incidence. The second emphasis is on the acoustic radiation torque per length. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a cylindrical fluid column trapped in air because of the significant acoustic impedance mismatch at the particle boundary. Based on the rigorous partial-wave series expansion method in cylindrical coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape, such as Chebyshev cylindrical particles with a small deformation, stadiums (with oval shape), or other non-circular geometries.

42 ENGINEERING↗
DOE OSTI2015

Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves

The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elements require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Dynamic field theory and equations of motion in cosmology

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress–energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1980

On the pressure field of nonlinear standing water waves

The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.

Schwartz, L. W.↗
NASA NTRS1980

Radar altimeter mean return wave forms from near-normal-incidence ocean surface scattering

For a nearly Gaussian transmitted pulse shape scattered from a nearly Gaussian distributed sea surface, a small argument series expansion of one term lead to a several term power series expression for the mean return waveform. Specific expressions are given for the first four terms. These results, which require less computer time than numerical convolution, are useful for data analysis from current or past radar altimeters and for design studies of future systems. Several representative results are presented for an idealized Seasat-1 radar altimeter.

Hayne, G. S.↗
NASA NTRS1983

Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

Fu, L. S.↗
NASA NTRS1983

Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

Zhong, W. F.↗
NASA NTRS1981

Noise suppression characteristics of peripherally segmented duct liners

The acoustic fields and transmission losses produced in semi-infinite circular ducts with peripherally segmented liners are analyzed using a series expansion of hard-wall duct modes. The coefficients of the series are computed using Galerkin's method. Unlike finite element approaches, this analysis includes the effects of realistic sources and the number of peripheral strips need not be small. It is shown that peripherally segmented liners redistribute the acoustic energy in waves composed of only a single circumferential mode at the source into other waves which contain a multitude of circumferential modes in the lined section. The accuracy of eigenfunctions computed from the analysis was observed to increase as either the frequency or radial mode order increased. The transmission losses were found to be accurate at frequencies above the cut-on value of the first-order radial mode in a hard-wall duct. The results show that for plane wave sources, peripherally segmented liners may attenuate as much sound as an optimized uniform liner at the optimal point while giving more noise suppression at most other frequencies.

Watson, W. R.↗
NASA NTRS1982

Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation

Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.

Fu, L. S.↗
NASA NTRS1979

A new propagation method for the radial Schroedinger equation

A new method for propagating the solution of the radial Schroedinger equation is derived from a Taylor series expansion of the wavefunction and partial re-summation of the infinite series. Truncation of the series yields an approximation to the exact propagator which is applied to a model calculation and found to be highly convergent.

Devries, P. L.↗
NASA NTRS1993

A generalized Zel'dovich approximation to gravitational instability

The orbits of particles undergoing gravitational instability are parameterized by generalizing the Zel'dovich approximation to a series expansion of arbitrary accuracy in the nonlinear regime. The coefficients of this series are determined from an action principle, or, more generally, from moments of the equation of motion. It is shown that the series is more rapidly convergent than previous nonlinear approximations. The method therefore provides a practical means of determining particle orbits, even for highly nonlinear perturbations. As an alternative, we also outline how the nonlinear dynamics may be computed as a field theory in which the evolution of the density and the velocity is determined in fixed comoving Eulerian coordinates.

Giavalisco, M.↗