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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Analysis of kink band formation under compression

The kink band formation in unidirectional composites under compression is analyzed in the present paper. The kinematics of kink band formation is described in terms of a deformation tensor. Equilibrium conditions are then applied to relate the compression load to the deformation of fibers. Since the in situ shear behavior of the matrix resin is not known, an analysis-experiment correlation is used to find the shear failure strain in the kink band. The present analysis thus elucidates the mechanisms and identifies the controlling parameters, of compression failure.

Hahn, H. Thomas↗
NASA NTRS1987

Efficient 3-D finite element failure analysis of compression loaded angle-ply plates with holes

Finite element stress analysis and the tensor polynomial failure criterion predict that failure always initiates at the interface between layers on the hole edge for notched angle-ply laminates loaded in compression. The angular location of initial failure is a function of the fiber orientation in the laminate. The dominant stress components initiating failure are shear. It is shown that approximate symmetry can be used to reduce the computer resources required for the case of unaxial loading.

Burns, S. W.↗
NASA NTRS1988

Experimental verification of a secondary recirculation zone in a labyrinth seal

The existence of a secondary recirculation zone inside the cavities of a labyrinth seal operating at a Reynolds number of 15,000 and a Taylor number of 10,300 has been experimentally verified. A three-dimensional laser Doppler anemometer system was used to measure the complete mean velocity and Reynolds stress tensor distributions in the first, third, fifth and seventh cavities of a seven cavity labyrinth seal which had a clearance of 1.27 mm.

Morrison, G. L.↗
NASA NTRS1988

Embedding of attitude determination in n-dimensional spaces

The problem of attitude determination in n-dimensional spaces is addressed. The proper parameters are found, and it is shown that not all three-dimensional methods have useful extensions to higher dimensions. It is demonstrated that Rodriguez parameters are conveniently extendable to other dimensions. An algorithm for using these parameters in the general n-dimensional case is developed and tested with a four-dimensional example. The correct mathematical description of angular velocities is addressed, showing that angular velocity in n dimensions cannot be represented by a vector but rather by a tensor of the second rank. Only in three dimensions can the angular velocity be described by a vector.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1988

3-D laser anemometer measurements in a labyrinth seal

The flow field inside a seven cavity labyrinth seal with a 0.00127 m clearance was measured using a 3-D laser Doppler anemometer system. Through the use of this system, the mean velocity vector and the entire Reynolds stress tensor distributions were measured for the first, third, fifth, and seventh cavities of the seal. There was one large recirculation region present in the cavity for the flow condition tested, Re = 28,000 and Ta = 7,000. The axial and radial mean velocities as well as all of the Reynolds stress term became cavity independent by the third cavity. The azimuthal mean velocity varied from cavity to cavity with its magnitude increasing as the flow progressed downstream.

Morrison, G. L.↗
NASA NTRS1988

3-D laser anemometer measurements in an annular seal

The flow field inside an annular seal with a 0.00127 m clearance was measured using a 3-D laser Doppler anemometer system. Through the use of this system, the mean velocity vector and the entire Reynolds stress tensor distributions were measured for the entire length of the seal (0.0373 m). The seal was operated at a Reynolds number of 27,000 and a Taylor number of 6,600.

Morrison, G. L.↗
NASA NTRS1987

A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations

Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.

Shay, R. M., Jr.↗
NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Baritzhack, Itzhack Y.↗
NASA NTRS1989

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Sarkar, Sutanu↗
NASA NTRS1989

On curve and surface stretching in turbulent flow

Cocke (1969) proved that in incompressible, isotropic turbulence the average material line (material surface) elements increase in comparison with their initial values. Good estimates of how much they increase in terms of the eigenvalues of the Green deformation tensor were rigorously obtained.

Etemadi, Nassrollah↗
NASA NTRS1989

On the Nature of Navier-stokes Turbulence

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The solutions, separate exponentially with time, having a positive Liapunov exponent. Thus the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number is reduced. Several qualitatively different flows are noted. These are, fully chaotic, complex period, weakly chaotic, simple periodic, and fixed-point. Of these, only the fully chaotic flows are classified as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, is both time-dependent and aperiodic. Turbulent solutions are obtained in which energy cascades from large to small-scale motions. In general, the spectral energy transfer takes place between wavenumber bands that are considerably separated. The special transfer can occur either as a result of nonlinear turbulence self-interaction or by interaction of turbulence with mean gradients. Turbulent systems are compared with those studied in kinetic theory. The two types of systems are fundamentally different (continuous and dissipative as opposed to discrete and conservative), but there are similarities. For instance, both are nonlinear and show sensitive dependence on initial conditions. Also, the turbulent and molecular stress tensors are identical if the macroscopic velocities for the turbulent stress are replaced by molecular velocities.

Deissler, Robert G.↗
NASA NTRS1989

A preliminary compressible second-order closure model for high speed flows

A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.

Speziale, Charles G.↗
NASA NTRS1988

The single crystal elastic constants of hexagonal SiC to 1000 C

The relationships between the sound velocities in the cubic and hexagonal crystal structures and the tensor transformations for the two structures are applied to determine the elastic stiffnesses for the hexagonal structures of SiC to 1000 C. These results are then applied to calculate the polycrystalline elastic moduli, E and G, and their temperature variations. The calculated values for E and G at 20 C are 420 and 180 GPa; for (dE/dT) and (dG/dT), the values are -0.020 and -0.007 GPa/C, respectively.These agree well with published experimental values for E and G of dense polycrystalline alpha silicon carbides.

Li, Z.↗
NASA NTRS1988

Fundamental problem in computing radiating flow fields with thick shock waves

Possible reasons for the failure of the Navier-Stokes equations to yield realistic profiles of the temperature and density through the structure of a hypersonic shock wave are investigated. Models for bulk viscosity in a monatomic gas are examined which yield a realistic thickness for the shock-wave density profile, but not the temperature profile, and hence are not satisfactory. A tentative computational model for nitrogen is explored which yields considerably more realistic results than the Navier-Stokes equations. This model involves a nonlinear stress-strain tensor, nonlinear heat flux vector, and nonequilibrium rotational energy.

Chapman, Dean R.↗
NASA NTRS1988

Electromagnetic wave scattering from some vegetation samples

For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite lenght. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle, and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements.

Karam, Mostafa A.↗
NASA NTRS1988

A cumulative damage model for continuous fiber composite laminates with matrix cracking and interply delaminations

The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.

Allen, David H.↗
NASA NTRS1989

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Baker, A. J.↗
NASA NTRS1989

An implicit and stiffly stable finite element CFD algorithm for unsteady aerodynamics

A stable and accurate finite element CFD algorithm for hyperbolic/incompletely parabolic conservation law systems is described and verified. It combines a Taylor weak statement FEM, an optimal implicit Runge-Kutta time integration algorithm, and a matrix tensor product approximate factorization linear algebra procedure. The results of computational experiments show that the developed algorithm is robust.

Baker, A. J.↗