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At least 235 records · Page 13

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NASA NTRS1986

MHD bending waves in a current sheet

Transverse MHD bending waves are considered in an isothermal and compressible two-dimensional current sheet of finite thickness in which the magnetic field changes direction and strength. The general form of the wave equation is obtained. It is shown that rotation of the magnetic field across the current sheet prevents the existence of singular points so that continuous spectrum solutions and the concomitant wave decay disappear. Instead, normal modes exist and closed integral solution for arbitrary current sheet structure are found. The results are discussed in terms of small-scale waves on the heliospheric current sheet.

Musielak, Z. E.↗

NASA NTRS1990

Development of a linearized unsteady aerodynamic analysis for cascade gust response predictions

A method for predicting the unsteady aerodynamic response of a cascade of airfoils to entropic, vortical, and acoustic gust excitations is being developed. Here, the unsteady flow is regarded as a small perturbation of a nonuniform isentropic and irrotational steady background flow. A splitting technique is used to decompose the linearized unsteady velocity into rotational and irrotational parts leading to equations for the complex amplitudes of the linearized unsteady entropy, rotational velocity, and velocity potential that are coupled only sequentially. The entropic and rotational velocity fluctuations are described by transport equations for which closed-form solutions in terms of the mean-flow drift and stream functions can be determined. The potential fluctuation is described by an inhomogeneous convected wave equation in which the source term depends on the rotational velocity field, and is determined using finite-difference procedures. The analytical and numerical techniques used to determine the linearized unsteady flow are outlined. Results are presented to indicate the status of the solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described herein leads to very efficient predictions of cascade unsteady aerodynamic response phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Verdon, Joseph M.↗

NASA NTRS1981

Equations of motion for a free-electron laser with an electromagnetic pump field and an axial electrostatic field

The equations of motion for a free-electron laser (FEL) with an electromagnetic pump field and a static axial electric field are derived using a Hamiltonian formalism. Equations governing the energy transfer between the electron beam and each of the electromagnetic fields are given, and the phase shift for each of the electromagnetic fields is derived from a linearized Maxwell wave equation. The relation between the static axial electric field and the resonant phase is given. Laser gain and the fraction of the electron energy converted to photon energy are determined using a simplified resonant particle model. These results are compared to those of a more exact particle simulation code.

Hiddleston, H. R.↗

NASA NTRS1974

The influence of the computational mesh on accuracy for initial value problems with discontinuous or nonunique solutions

Discontinuous, or weak, solutions of the wave equation, the inviscid form of Burgers equation, and the time-dependent, two-dimensional Euler equations are studied. A numerical method of second-order accuracy in two forms, differential and integral, is used to calculate the weak solutions of these equations for several initial value problems, including supersonic flow past a wedge, a double symmetric wedge, and a sphere. The effect of the computational mesh on the accuracy of computed weak solutions including shock waves and expansion phenomena is studied. Modifications to the finite-difference method are presented which aid in obtaining desired solutions for initial value problems in which the solutions are nonunique.

Maccormack, R. W.↗

NASA NTRS1990

Long-time behaviour of absorbing boundary conditions

A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.

Engquist, B.↗

NASA NTRS1981

Analytical and experimental investigation of the propagation and attenuation of sound in extended reaction lined ducts

Results are presented of an analytical and experimental study of the attenuation and propagation of harmonically excited sound waves in an extended reaction lined cylindrical duct. The duct geometry considered consisted of an annular outer region of bulk material surrounding an inner cylinder of air. The coupled wave equations governing the motion of the sound in both the inner and annular regions were solved numerically. The numerically predicted attenuation and propagation constants were in excellent agreement with measured values using Kevlar as the liner material for plane-wave mode (0,0) excitation over the frequency from 100 to 7,000 Hz. Although the numerical model was verified using Kevlar, it can be used with any fibrous constructed bulk liner. The results of this study demonstrate that a good start has been made on the numerical modelling of the acoustic performance of extended reaction liners.

Hersh, A. S.↗

NASA NTRS1988

Far field boundary conditions for computation over long time

A new class of computational far field boundary conditions for hyperbolic partial differential equations is developed. These boundary conditions combine properties of absorbing boundary conditions for transient solutions and properties of far field boundary conditions for steady-state problems. The conditions can be used to limit the computational domain when both traveling waves and evanescent waves are present. Boundary conditions for scalar wave equations are derived and analyzed. Extensions to systems of equations are discussed and results from numerical experiments are presented.

Engquist, Bjorn↗

NASA NTRS1990

Matrix-based, finite-difference algorithms for computational acoustics

A compact numerical algorithm is introduced for simulating multidimensional acoustic waves. The algorithm is expressed in terms of a set of matrix coefficients on a three-point spatial grid that approximates the acoustic wave equation with a discretization error of O(h exp 5). The method is based on tracking a local phase variable and its implementation suggests a convenient coordinate splitting along with natural intermediate boundary conditions. Results are presented for oblique plane waves and compared with other procedures. Preliminary computations of acoustic diffraction are also considered.

Davis, Sanford↗

NASA NTRS1983

Effect of flow on the acoustic performance of extended reaction lined ducts

A model is developed for the effects of uniform and boundary-layer mean flow on the attenuation and propagation of harmonically excited sound waves in an extended reaction lined cylindrical duct. A duct geometry consisting of an annular outer region of bulk material surrounding an inner cylinder of air is utilized. A numerical solution is obtained for the coupled wave equations governing the motion of the sound in both the inner and annular regions. It is found that the numerically predicted attenuation and propagations constants are in excellent agreement with measured values using Kevlar as the liner material for plane-wave mode (O,O) excitation over a wide range of mean flows and sound frequency. The boundary-layer effects are determined to be unimportant, at least for plane-wave sound. In addition, numerical studies indicate small differences between the use of either the radial velocity or the radial displacement boundary conditions.

Hersh, A. S.↗

NASA NTRS1991

Computational dispersion properties of horizontal staggered grids for atmospheric and ocean models

The computational dispersion properties of horizontally and time-horizontally staggered grids utilizing corresponding centered-difference techniques for approximation of the adjustment, or gravity wave equations, are examined in terms of their group velocity characteristics. Results are acquired for oceanic and atmospheric models, the former being characterized by a much smaller Rossby radius of deformation. For all grids considered additional filtering is required to control and even eliminate waves with poor computational dispersion characteristics. Computational dispersion properties along with other computational characteristics and requirements give some guidance for an optimal selection of an appropriate grid for an ocean or atmospheric model.

Fox-Rabinovitz, Michael S.↗

NASA NTRS1974

Topics in structural dynamics: Nonlinear unsteady transonic flows and Monte Carlo methods in acoustics

The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.

Haviland, J. K.↗

NASA NTRS1989

An Entropy-Based Approach to Nonlinear Stability

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Merriam, Marshal L.↗

NASA NTRS1977

The generation of gravitational waves. II - The postlinear formalism revisited

Two different versions of the Green's function for the scalar wave equation in weakly curved spacetime (one due to DeWitt and DeWitt, the other to Thorne and Kovacs) are compared and contrasted; and their mathematical equivalence is demonstrated. Then the DeWitt-DeWitt Green's function is used to construct several alternative versions of the Thorne-Kovacs postlinear formalism for gravitational-wave generation. Finally it is shown that, in calculations of gravitational bremsstrahlung radiation, some of our versions of the postlinear formalism allow one to treat the interacting bodies as point masses, while others do not.

Crowley, R. J.↗

NASA NTRS1990

Acoustic waves superimposed on incompressible flows

The use of incompressible approximations in deriving solutions to the Lighthill wave equation was investigated for problems where an analytical solution could be found. A particular model problem involves the determination of the sound field of a spherical oscillating bubble in an ideal fluid. It is found that use of incompressible boundary conditions leads to good approximations in the important region of high acoustic wave number.

Hodge, Steve↗

NASA NTRS1975

The generation of gravitational waves. 2: The post-linear formalism revisited

Two different versions of the Green's function for the scalar wave equation in weakly curved spacetime (one due to DeWitt and DeWitt, the other to Thorne and Kovacs) are compared and contrasted; and their mathematical equivalence is demonstrated. The DeWitt-DeWitt Green's function is used to construct several alternative versions of the Thorne-Kovacs post-linear formalism for gravitational-wave generation. Finally it is shown that, in calculations of gravitational bremsstrahlung radiation, some of our versions of the post-linear formalism allow one to treat the interacting bodies as point masses, while others do not.

Crowley, R. J.↗

NASA NTRS1992

Aerodynamics of loaded cascades in subsonic flows subject to unsteady three-dimensional vortical disturbances

A highly efficient numerical method is developed for three-dimensional, periodic, vortical flows around a cascade of loaded airfoils. The method linearizes Euler's equations about the mean flow of the cascade and thus fully accounts for the effects of distortion of the vortical disturbances as they propogate and interact with the cascade mean flow. The numerical scheme is based on splitting the unsteady velocity into vortical and potential parts. The latter is governed by a non-constant coefficient inhomogeneous convective wave equation. A new and computationally suitable out-flow conditions are derived and avoid the difficulties associated with the singular velocity downstream. Solutions were obtained in the frequency domain by using a body-fitted coordinate system. Results are presented to demonstrate the effects of the out-flow boundary conditions, cascade spacing, mean blade loading and gust upstream conditions on the aerodynamics response and unsteady pressure field of a cascade.

Fang, J.↗

NASA NTRS1991

A finite-difference, frequency-domain numerical scheme for the solution of the linearized unsteady Euler equations

A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method, that is presented, fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is generally very good for reduced frequencies ranging from 0 up to 4.

Scott, James R.↗

NASA NTRS1975

Propagation of Sound at Moderate and High Intensities in Absorbent and Hard-Walled Cylindrical Ducts

The propagation of plane wave and higher order acoustic modes in both hard-walled and absorbent cylindrical ducts was studied at moderate sound intensities where the linear wave equation is valid, and at high intensities where nonlinear effects can be observed. The experiments were conducted with an anechoically terminated twelve-inch inside-diameter transite pipe. Various types of sound sources were mounted at one end of the duct to generate the desired acoustic fields within the duct. Arrays of conventional loudspeakers were used to generate plane waves and higher order acoustic modes at moderate intensities, and an array of four high intensity electro-pneumatic sound sources was used for the experiments in the nonlinear region. The attenuation of absorbent liners made of several different materials was obtained at moderate intensities for both plane waves and high order modes. It was found that the characteristics of the liners studied did not change appreciably at high intensities.

Mcdaniel, Oliver Herbert↗