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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

qSmoothed particle interpolation

Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of a nonhydrodynamical nature. Under this approach, SPH is viewed as strickly as interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogenous sound speed and (2) Burger's equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite-difference methods. It is shown that the power of SPI arises when the smoothing particles are free to move.

Laguna, Pablo↗
DOE OSTI2014

Phononic crystals and elastodynamics: Some relevant points

In the present paper we review briefly some of the first works on wave propagation in phononic crystals emphasizing the conditions for the creation of acoustic band-gaps and the role of resonances to the band-gap creation. We show that useful conclusions in the analysis of phononic band gap structures can be drawn by considering the mathematical similarities of the basic classical wave equation (Helmholtz equation) with Schrödinger equation and by employing basic solid state physics concepts and conclusions regarding electronic waves. In the second part of the paper we demonstrate the potential of phononic systems to be used as elastic metamaterials. This is done by demonstrating negative refraction in phononic crystals and subwavelength waveguiding in a linear chain of elastic inclusions, and by proposing a novel structure with close to pentamode behavior. Finally the potential of phononic structures to be used in liquid sensor applications is discussed and demonstrated.

36 MATERIALS SCIENCE↗
NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗
NASA NTRS1994

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Goorjian, Peter M.↗
NASA NTRS1994

Numerical Simulations of Light Bullets, Using the Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1995

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1994

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
DOE OSTI2021

Separability in consistent truncations

The separability of the Hamilton-Jacobi equation has a well-known connection to the existence of Killing vectors and rank-two Killing tensors. This paper combines this connection with the detailed knowledge of the compactification metrics of consistent truncations on spheres. The fact that both the inverse metric of such compactifications, as well as the rank-two Killing tensors can be written in terms of bilinears of Killing vectors on the underlying “round metric,” enables us to perform a detailed analyses of the separability of the Hamilton-Jacobi equation for consistent truncations. We introduce the idea of a separating isometry and show that when a consistent truncation, without reduction gauge vectors, has such an isometry, then the Hamilton-Jacobi equation is always separable. When gauge vectors are present, the gauge group is required to be an abelian subgroup of the separating isometry to not impede separability. We classify the separating isometries for consistent truncations on spheres, S n , for n = 2, …, 7, and exhibit all the corresponding Killing tensors. These results may be of practical use in both identifying when supergravity solutions belong to consistent truncations and generating separable solutions amenable to scalar probe calculations. Finally, while our primary focus is the Hamilton-Jacobi equation, we also make some remarks about separability of the wave equation.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Analytic numerical solutions for shock waves

Study of weak solutions of simple wave equation, inviscid Burgers equation, and Euler equations has resulted in technique for accurate prediction of shock waves occurring in inviscid supersonic flows.

Maccormack, R. W.↗
NASA NTRS1984

Magneto-atmospheric waves from a localized source

A technique developed by Lighthill (1960, 1965, and 1967) for finding the asymptotic solution of an inhomogeneous wave equation with constant coefficients is applied to the study of wave propagation in magneto-atmospheres. The geometry of the wavenumber surface plays an important role in determining the generation and propagation of various types of magneto-atmospheric waves from a localized forcing region. Examples of these wavenumber surfaces are exhibited for various magnetic-field strengths and wave frequencies. The asymptotic far field is tabulated for a time-harmonic spatially Gaussian localized forcing term.

Adam, J. A.↗
NASA NTRS1987

Density fluctuations induced by nonlinear Alfven waves

The generation of plasma density fluctuations by nonlinear Alfven waves is considered. Of particular interest is the modification to the 'static approximation', describing the relationship between wave intensity and plasma density, when the Alfven wave packet is rapidly steepening. The study concentrates on a forced wave equation for the plasma density, which yields the static approximation in a select approximnation. An analytic solution to this equation is obtained for a reasonable model of a steeping wave packet. The principal results are: (1) the static approximation should give a surprisingly robust description of the coupling between Alfven wave intensity and plasma density; (2) departures of the plasma density perturbation from the static approximation result are determined by a parameter that is a simple function of the wave amplitude and plasma beta; (3) for rapidly evolving wave packets, the position of maximum density change is displaced from that of maximum wave intensity, and (4) the magnitude of the density fluctuation will not be much different than the static approximation estimate.

Spangler, Steven R.↗
DOE OSTI2017

Intersection Waves: INTERSECTION WAVES

Intersections in a fracture network control the connectivity of the flow paths through rock. The long near-linear geometric nature of fractures makes them difficult to identify and characterize. We present a new type of elastic wave, an intersection wave, which travels along an intersection and is sensitive to the coupling between two orthogonal fractures that define the intersection. Group theory for C 2v and C 4v point groups predicts sets of propagating elastic waves confined to the fracture intersection. Along with the use of the wave equation and displacement discontinuity boundary conditions, the dispersion relationships for intersection waves are predicted. Experimental ultrasonic measurements on a nonwelded linear intersection between two orthogonal, synthetic fractures in aluminum confirm the existence of multiple modes that travel between the speed of wedge waves (sub-Rayleigh waves) when the intersection is completely, and bulk shear waves, when the intersection is closed, as predicted by theory. Between these two limits, the intersection behaves as a nonwelded contact and yields these new intersection waves that are dispersive and sensitive to the coupling along the intersection. Intersection waves provide the foundation for new geophysical approaches for characterizing the hydraulic connectivity of fracture networks.

58 GEOSCIENCES↗
DOE OSTI2014

Inertial confinement fusion based on the ion-bubble trigger

Triggering the ion-bubble in an inertial confinement fusion, we have developed a novel scheme for the fast ignition. This scheme relies on the plasma cavitation by the wake of an intense laser pulse to generate an ion-bubble. The bubble acts both as an intense electron accelerator and as an electron wiggler. Consequently, the accelerated electrons trapped in the bubble can emit an intense tunable laser light. This light can be absorbed by an ablation layer on the outside surface of the ignition capsule, which subsequently drills it and thereby produces a guide channel in the pellet. Finally, the relativistic electron beam created in the bubble is guided through the channel to the high density core igniting the fusion fuel. The normalized beam intensity and beam energy required for triggering the ignition have been calculated when core is heated by the e-beam. In addition, through solving the momentum transfer, continuity and wave equations, a dispersion relation for the electromagnetic and space-charge waves has been analytically derived. The variations of growth rate with the ion-bubble density and electron beam energy have been illustrated. It is found that the growth rates of instability are significantly controlled by the ions concentration and the e-beam energy in the bubble.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Sensitive Detection: Photoacoustics, Thermography, and Optical Radiation Pressure

Research during the granting period has been carried out in several areas concerned with sensitive detection. An infrared pyrometer based on the photoacoustic effect has been developed. The sensitivity of this instrument to temperature differentials has been shown to be 50 mK. An investigation of transients that accompany photoacoustic waves generated by pulsed lasers has been carried out. Experiments have shown the existence of the transients, and a theory based on rapid heat diffusion has been developed. The photoacoustic effect in one dimension is known to increase without bound (in the linear acoustics regime) when an optical beam moves in a fluid at the sound speed. A solution to the wave equation for pressure has been found that describes the photoacoustic effect in a cell where an infrared optical grating moves at the sound speed. It was shown that the amplification effect exists along with a cavity resonance that can be used to great advantage in trace gas detection. The theory of the photoacoustic effect in a structure where the acoustic properties periodically vary in a one-dimensional based has been formulated based on solutions to a Mathieu equation. It was found that it is possible to excite photoacoustic waves within the band gaps to produce large amplitude acoustic waves. The idea of self-oscillation in a photoacoustic cell using a continuous laser has been investigated. A theory has been completed showing that in a compressive wave, the absorption increases as a result of the density increase leading to further absorption and hence an increased amplitude photoacoustic effect with the result that in a resonator, self-oscillation can place. Experiments have been carried out where irradiation of a suspension of absorbing carbon particles with a high power laser has been shown to result in cavitation luminescence. That is, following generation of CO and H 2 from the carbon particles through the carbon-steam reaction, an expanding gas bubble is produced, which during the phase where the bubble collapses, a sonoluminescent flash is produced. Work on the voltage generated by a spherical, colloidal object irradiated with an acoustic wave has been determined. The theory of X-ray imaging using a grating to generate a spatially heterodyned image has been formulated. The properties of X-ray images taken with a grating placed before the object and the resulting image Fourier transformed and filtered has been determined. The method essentially heterodynes the spatial component of the object in the image which can be used to eliminate scatter that degrades contrast. Another area of investigation is the motion of the components in a separation method known as thermal diffusion, or the Soret effect. By exploring the mathematics of the effect, it was found that the underlying mechanism of the separation is propagation of a shock whose features are masked typically by the effects of viscosity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1981

Recent advances in the development of implicit schemes for the equations of fluid dynamics

Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of one-leg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the P-dimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.

Warming, R. F.↗
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 NTRS1988

Analysis of nonuniform subsonic flows about a row of moving blades

The motion of a nonuniform flow about a row of moving blades is modeled as that of a three-dimensional rotational disturbance convected by the mean flow. The aerodynamic theories for such flows are reviewed for both linearly propagating disturbances and disturbances distorted by the mean flow. Linear theories results are examined to assess the effects of the gust variables, the Mach number, and the blade spacing, on the unsteady blade response. For loaded blades, the upstream disturbances are distorted by the blade mean flow. For a potential mean flow, the governing equations can be reduced to a single inhomogeneous nonconstant coefficient convective wave equation. A numerical procedure is developed using an elliptic grid system. The accuracy of the solutions strongly depends on the far-field radiation condition and the optimum determination of the grid system. Solutions are presently obtained for thick symmetric airfoils in three-dimensional gusts.

Atassi, H. M.↗