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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 199 records · Page 11
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NASA NTRS1971

Analysis of transient, linear wave propagation in shells by the finite difference method

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Geers, T. L.↗
NASA NTRS1972

A finite difference method for predicting supersonic turbulent boundary layer flows with tangential slot injection

An implicit finite difference method has been applied to tangential slot injection into supersonic turbulent boundary layer flows. In addition, the effects induced by the interaction between the boundary layer displacement thickness and the external pressure field are considered. In the present method, three different eddy viscosity models have been used to specify the turbulent momentum exchange. One model depends on the species concentration profile and the species conservation equation has been included in the system of governing partial differential equations. Results are compared with experimental data at stream Mach numbers of 2.4 and 6.0 and with results of another finite difference method. Good agreement was generally obtained for the reduction of wall skin friction with slot injection and with experimental Mach number and pitot pressure profiles. Calculations with the effects of pressure interaction included showed these effects to be smaller than effects of changing eddy viscosity models.

Miner, E. W.↗
NASA NTRS1971

Similarity and generalized finite-difference solutions of parabolic partial differential equations.

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Clausing, A. M.↗
NASA NTRS1972

Study of X-ray diffraction on aging alloys with different degrees of volume discrepancy between the precipitation phase and the matrix

Study of the diffraction patterns of X rays diffracted by dispersion-hardened alloys with various degrees of difference between the specific atomic volumes of their precipitation phases and matrices. Experiments were performed on aging alloys KhN77TIuR (nimonic) and KhN67VMTIuO, which have the same types of gamma solid solutions and precipitating gamma prime phases, but differ considerably with respect to the volume factor. It is found that in the decay of supersaturated solid solutions for which the difference between the specific atomic volumes of the precipitation phase and the matrix is small (alloy KhN67VMTIuO) the nature of the intensity distribution of the diffraction lines remains practically unchanged regardless of the aging, while in cases where the volume discrepancy is large (alloy KhN77TIuR) significant changes in the appearance of the diffraction lines are recorded.-

Gitgarts, M. I.↗
NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. II.

Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.

Baxley, J. V.↗
NASA NTRS1973

A difference theory for noise propagation in an acoustically lined duct with mean flow

A finite difference formulation is presented for sound propagation in a two-dimensional straight soft-walled duct with uniform flow. The difference analysis is developed in terms of complex notation. The governing acoustic difference equations and the appropriate displacement boundary conditions associated with uniform flow are presented for the sound attenuation in straight hard and soft-walled ducts. At present the finite Mach number case is solved only for the one-dimensional hard walled duct.

Baumeister, K. J.↗
NASA NTRS1973

A difference theory for noise propagation in an acoustically lined duct with mean flow.

A finite difference formulation is presented for sound propagation in a two-dimensional straight soft-walled duct with uniform flow. The difference analysis is developed in terms of complex notation. The governing acoustic difference equations and the appropriate displacement boundary conditions associated with uniform flow are presented. Example calculations are presented for the sound attenuation in straight hard and soft-walled ducts. At present the finite Mach number case is solved only for the one-dimensional hard walled duct.

Baumeister, K. J.↗
NASA NTRS1973

Convergence of finite difference transient response computations for thin shells.

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Sobel, L. H.↗
NASA NTRS1974

The modified equation approach to the stability and accuracy analysis of finite-difference methods

The stability and accuracy of finite-difference approximations to simple linear partial differential equations are analyzed by studying the modified partial differential equation. Aside from round-off error, the modified equation represents the actual partial differential equation solved when a numerical solution is computed using a finite-difference equation. The modified equation is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations. The connection between 'heuristic' stability theory based on the modified equation approach and the von Neumann (Fourier) method is established. In addition to the determination of necessary and sufficient conditions for computational stability, a truncated version of the modified equation can be used to gain insight into the nature of both dissipative and dispersive errors.

Warming, R. F.↗
NASA NTRS1974

Stability properties of functional difference equations

Hale and Cruz (1970) have defined the concept of a stable difference operator, and have found that this class of operators is sometimes 'super sensitive' to perturbations. In the present paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations. Also, the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions, and essentially bounded functions.

Melvin, W. R.↗
NASA NTRS1974

The use of multispectral difference data for urban change detection

The current work describes an experiment in which ERTS-1 digital multispectral scanner data from two times was used to detect change in an urban scene. The computer analysis implementation approach explored here was to register image data from the two times and to subtract the data to form multispectral difference images. The difference imagery was then analyzed using statistical pattern recognition to separate and classify different types of change. Construction was successfully detected.

Anuta, P. E.↗
NASA NTRS1976

Strong scintillations in astrophysics. 4. Cross-correlation between different frequencies and finite bandwidth effects

The cross correlation of the intensity fluctuations between different frequencies and finite bandwidth effects on the intensity correlations based on the Markov approximation were calculated. Results may be applied to quite general turbulence spectra for an extended turbulent medium. Calculations of the cross-correlation function and of finite bandwidth effects are explicitly carried out for both Gaussian and Kolmogorov turbulence spectra. The increases of the correlation scale of intensity fluctuations are different for these two spectra and the difference can be used to determine whether the interstellar turbulent medium has a Gaussian or a Kolmogorov spectrum.

Lee, L. C.↗
NASA NTRS1976

Strong scintillations in astrophysics. IV - Cross-correlation between different frequencies and finite bandwidth effects

The cross-correlation of the intensity fluctuations between different frequencies and finite-bandwidth effects on the intensity correlations are calculated based on the Markov approximation. The results may be applied to quite general turbulence spectra for an extended turbulent medium. Calculations of the cross-correlation function and of finite-bandwidth effects are explicitly carried out for both Gaussian and Kolmogorov turbulence spectra. The increases of the correlation scale of intensity fluctuations are different for these two spectra, and the difference can be used to determine whether the interstellar turbulent medium has a Gaussian or a Kolmogorov spectrum.

Lee, L. C.↗
NASA NTRS1977

Finite-difference theory for sound propagation in a lined duct with uniform flow using the wave envelope concept

Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.

Baumeister, K. J.↗
NASA NTRS1977

High resolution 10 mu spectrometry at different planetary latitudes. A practical Hadamard transform spectrometer for astronomical application

Infrared observations at different latitudes were studied in order to obtain spectra in the 10 micrometers region to understand differences in chemical composition or physical structure of the optical features. In order to receive such spectra of a rotating planet, simultaneous observations at different latitudes were made. A Hadamard transform spectrometer with 15 entrance slits was used to obtain 15 simultaneous spectra, at a resolution of 0.01 micrometers. The spectral band covered contained 255 spectral elements.

Tai, M. H.↗
NASA NTRS1978

Numerical computation of transonic flows by finite-element and finite-difference methods

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Hafez, M. M.↗
NASA NTRS1979

A time dependent difference theory for sound propagation in ducts with flow

A time dependent numerical solution of the linearized continuity and momentum equation was developed for sound propagation in a two dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic difference equations and boundary conditions were developed along with a numerical determination of the maximum stable time increments. A harmonic noise source radiating into a quiescent duct was analyzed. This explicit iteration method then calculated stepwise in real time to obtain the transient as well as the steady state solution of the acoustic field. Example calculations were presented for sound propagation in hard and soft wall ducts, with no flow and plug flow. Although the problem with sheared flow was formulated and programmed, sample calculations were not examined. The time dependent finite difference analysis was found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.

Baumeister, K. J.↗
NASA NTRS1979

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Ehlers, F. E.↗