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At least 235 records · Page 13

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NASA NTRS1977

Aerodynamic sound in a relaxing medium

A theory of aerodynamic sound propagation, when inhomogeneities characterized by a relaxation process are present in both the source and propagation region, is formulated. The details of the relaxation process need not be specified at the outset, although the relaxation process is characterized by a relaxation time and by an equilibrium and a frozen sound speed in a propagation region which is otherwise in equilibrium. Propagation is described in terms of a D'Alembertian characterized by the frozen sound speed relaxing toward one characterized by the equilibrium sound speed, while the source is interpreted in terms of a frozen Lighthill stress tensor relaxing toward the equilibrium stress tensor. An appropriate Green's function for the three-dimensional relaxing wave propagation operator is used to construct an exact integral for the aerodynamic sound. The sound generated far from the source is then estimated in terms of the aerodynamic sound source.

Liu, J. T. C.↗

NASA NTRS1978

On the rotation of elliptical galaxies

The tensor virial theorem is applied to models of early-type galaxies. First the theorem is applied to rotating elliptical galaxies whose constant-density surfaces are similar ellipsoids. A relationship is obtained between the observed rotations and the forms of generally triaxial galaxies. By applying the results of Robert (1962) to the evaluation of the components of the Chandrasekhar tensor which occurs in this relationship, it is found that the form of a galaxy that lacks global velocity anisotropy uniquely determines the ratio of its rotational and random kinetic energies independently of the radial density profile of that galaxy. A distribution of three-dimensional prolate spheroids is derived which accounts for the observed distribution of ellipticities reported by Sandage, Freeman, and Stokes (1970). This is then used to derive curves giving the expected frequency of occurrence of galaxies of given rotational velocities for each of a number of different apparent elongations on the sky. It is found that if elliptical galaxies are prolate, there should be little correlation between apparent ellipticity and rotation velocity.

Binney, J.↗

NASA NTRS1979

A split finite element algorithm for the compressible Navier-Stokes equations

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Baker, A. J.↗

NASA NTRS1979

On nuclear spin statistics in rotational transition intensities in tetrahedral AB4 molecules

A general expression is derived for the integrated intensity of rotational transitions in the vibronic ground state of tetrahedral molecules, taking into account the nuclear spin statistics. It is shown that the ratio of this expression to previously published spin-free integrated intensities depends only on the tensor character N of the operator driving the transition, the appropriate rotational quantum numbers J and J', and the nuclear spin of the identical nuclei. Tables are given for N = 3, 4 and J no more than 50, which enable the calculation of integrated intensities for octopole and hexadecapole collision-induced dipole-moment transitions, centrifugal-distortion-induced dipole-moment transitions, and centrifugal-distortion-induced anisotropic-polarizability-tensor Raman transitions.

Rosenberg, A.↗

NASA NTRS1979

Mathematical Modeling of Diverse Phenomena

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

Howard, J. C.↗

NASA NTRS1980

Alternatives for jet engine control

Nonlinear modeling researches involving the use of tensor analysis are presented. Progress was achieved by extending the studies to a controlled equation and by considering more complex situations. Included in the report are calculations illustrating the modeling methodology for cases in which variables take values in real spaces of dimension up to three, and in which the degree of tensor term retention is as high as three.

Sain, M. K.↗

NASA NTRS1979

Nonlinear temperature dependent failure analysis of finite width composite laminates

A quasi-three dimensional, nonlinear elastic finite element stress analysis of finite width composite laminates including curing stresses is presented. Cross-ply, angle-ply, and two quasi-isotropic graphite/epoxy laminates are studied. Curing stresses are calculated using temperature dependent elastic properties that are input as percent retention curves, and stresses due to mechanical loading in the form of an axial strain are calculated using tangent modulii obtained by Ramberg-Osgood parameters. It is shown that curing stresses and stresses due to tensile loading are significant as edge effects in all types of laminate studies. The tensor polynomial failure criterion is used to predict the initiation of failure. The mode of failure is predicted by examining individual stress contributions to the tensor polynomial.

Nagarkar, A. P.↗

NASA NTRS1979

Failure analysis of composite laminates with free edges

Linear elastic stress distributions obtained from a refined finite element mesh are used in conjunction with the tensor polynomial failure criterion to predict the initiation of failure in symmetric, finite-width graphite-epoxy laminates under tensile loading. Results are presented for a wide variety of laminates including: (+ and - theta)s angle-ply; cross-ply (0/90)s and (90/0)s; and quasi-isotropic (90/0/+ and - 45)s and (+ and -45/0/90)s. It is shown that the elastic stress distributions generally compare favorably with other published results, but also indicate improved satisfaction of the stress-free boundary conditions and indicate some differences in the singular behavior of selected stress components at the free edge. The tensor polynomial failure criterion is used to predict the location and mode of first failure. Examination of the individual terms of the polynomial indicates different modes of failure depending upon the laminate configuration.

Herakovich, C. T.↗

NASA NTRS1980

Space-time metrical fluctuations induced by cosmic turbulence

For a stochastic stress-energy tensor associated with cosmic turbulence, it is observed that Einstein's equations imply fluctuations in the space-time metric tensor. Such metrical fluctuations are shown to engender modified values for the average effective proper density and total pressure and thus to alter the solutions to the Friedman equations.

Rosen, G.↗

NASA NTRS1979

Calculation of three-dimensional turbulent subsonic flows in transition ducts

A method for computing three-dimensional turbulent subsonic flow in curved ducts is being developed. A set of tube-like surface oriented coordinates is employed for a general class of geometries applicable to subsonic diffusers with offset bends. The geometric formulation is complex and no previous treatment of this class of viscous flow problems is known to the authors. The duct centerline is a space curve specified by piecewise polynomials. A Frenet frame is located on the centerline at each axial location. The cross sections are described by superellipses imbedded in the Frenet frame. Duct surfaces are also coordinate surfaces, which greatly simplifies the boundary conditions. The resulting coordinates are nonorthogonal. An approximate set of governing equations is employed for viscous flows having strong flow in a primary flow direction. The derivation is coordinate invariant and the resulting equations are expressed in tensor form. These equations are solved by an efficient alternating direction implicit (ADI) method. This numerical method is generally stable and permits solution in difficult geometries using the general tensor formulation.

Levy, R.↗

NASA NTRS1981

Prediction of absolute infrared intensities for the fundamental vibrations of H2O2

Absolute infrared intensities are predicted for the vibrational bands of gas-phase H2O2 by the use of a hydrogen atomic polar tensor transferred from the hydroxyl hydrogen atom of CH3OH. These predicted intensities are compared with intensities predicted by the use of a hydrogen atomic polar tensor transferred from H2O. The predicted relative intensities agree well with published spectra of gas-phase H2O2, and the predicted absolute intensities are expected to be accurate to within at least a factor of two. Among the vibrational degrees of freedom, the antisymmetric O-H bending mode nu(6) is found to be the strongest with a calculated intensity of 60.5 km/mole. The torsional band, a consequence of hindered rotation, is found to be the most intense fundamental with a predicted intensity of 120 km/mole. These results are compared with the recent absolute intensity determinations for the nu(6) band.

Rogers, J. D.↗

NASA NTRS1981

Numerical simulation of a compressible homogeneous, turbulent shear flow

A direct, low Reynolds number, numerical simulation was performed on a homogeneous turbulent shear flow. The full compressible Navier-Stokes equations were used in a simulation on the ILLIAC IV computer with a 64,000 mesh. The flow fields generated by the code are used as an experimental data base, to examine the behavior of the Reynols stresses in this simple, compressible flow. The variation of the structure of the stresses and their dynamic equations as the character of the flow changed is emphasized. The structure of the tress tensor is more heavily dependent on the shear number and less on the fluctuating Mach number. The pressure-strain correlation tensor in the dynamic uations is directly calculated in this simulation. These correlations are decomposed into several parts, as contrasted with the traditional incompressible decomposition into two parts. The performance of existing models for the conventional terms is examined, and a model is proposed for the 'mean fluctuating' part.

Feiereisen, W. J.↗

NASA NTRS1982

Reynolds averaged Navier-Stokes computations of transonic flows The-state-of-the-art

The state of the art in computer simulations for transonic flowfields requiring solutions for the Navier-Stokes equations is assessed. It is noted that current simulations of transonic flowfields require comparisons with experimental results because the simulations are not free from discretization errors. Cases of turbulence are treated with weighted variables in a time-averaged scheme to yield Reynolds averaged Navier-Stokes equations. The turbulence is modeled in a first-order approach with a Reynolds stress tensor or a second-order approach where the tensor is obtained from the Navier-Stokes equations. The choice of coordinate systems and dependent variables for simulating the flow around airfoils is discussed, with particular attention to curvilinear coordinates. The determinations of boundary conditions is examined, along with numerical methods related to physical phenomena

Mehta, U.↗

NASA NTRS1982

Dipole-field sums and Lorentz factors for orthorhombic lattices, and implications for polarizable molecules

A method for computing the Lorentz tensor components in single crystals via rapidly convergent sums of Bessels functions is developed using the relationship between dipole-field sums and the tensor components. The Lorentz factors for simple, body-centered, and base-centered orthorhombic lattices are computed using this method, and the derivative Lorentz factors for simple orthorhombic lattices are also determined. Both the Lorentz factors and their derivatives are shown to be very sensitive to a lattice structure. The equivalent of the Clausius-Mossotti relation for general orthorhombic lattices is derived using the Lorentz-factor formalism, and the permanent molecular dipole moment is related to crystal polarization for the case of a ferroelectric of polarizable point dipoles. It is concluded that the polarization enhancement due to self-polarization familiar from classical theory may actually be a reduction in consequences of negative Lorentz factors in one or two lattice directions for noncubic crystals.

Purvis, C. K.↗

NASA NTRS1983

Ponderomotive force in a warm two-fluid plasma

A general expression for the ponderomotive force of electromagnetic field with slowly varying amplitude in a warm plasma is obtained in the collisionless two-fluid model. Compared to the existing expression obtained for a cold and stationary plasma, this result contains two additional terms for the general case. One of them is involved with the density gradient and the wavenumber derivative of the dielectric tensor of a plasma. Thus, for an inhomogeneous plasma, it accounts for the effects of spatial dispersion, hence of finite temperature of the plasma. The other term is proportional to the time derivative of the density and the frequency derivative of the dielectric tensor, and is nonzero unless the plasma is stationary or nondispersive. Inclusion of these new terms in the ponderomotive force will enable self-consistent analysis of the general behavior of nonlinear waves with finite wavelengths in a warm plasma.

Lee, N. C.↗

NASA NTRS1983

Kinematics of velocity and vorticity correlations in turbulent flow

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

Bernard, P. S.↗

NASA NTRS1984

Some properties of transient phenomena in the extra-tropical region and their importance in the seasonal mean flow

When studying data for one season, it is convenient to divide transient eddies into those of the synoptic time scale and those of lower frequency. Where the dividing line is placed is not crucial, but a 10-day period is used in a study of the 1979-1980 Northern Hemisphere winter. The synoptic time scale eddies exhibit maximum kinetic energy in stormtracks slightly downstream from and poleward of the Atlantic and Pacific jet maximum. An alternative approach is via the anisotropic part of the horizontal velocity correlation tensor, the axis of which gives the local orientation of the eddies and the magnitude a measure of the extension of the eddies. When the man velocity field is almost that of the plane waves, the horizontal group velocity relative to the mean field is also related to this tensor. The synoptic time scale eddies force the mean flow in the sense of reducing the baroclinic component in the upstream of the region of the stormtrack. The lower frequency eddies have a very different signature.

Hoskins, B. J.↗

NASA NTRS1983

An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface

Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.

Dagenhart, J. R↗