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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Temporal dynamics of the alignment of the turbulent stress and strain rate

We report that the flux of energy between scales in turbulence can be cast as the result of the interaction between a turbulent stress and a rate of strain. Efficient energy transfer requires that these two tensors be oriented properly relative to each other, but previous work has shown that the instantaneous alignment between them is poor. Here, we consider the temporal dynamics of this alignment in a direct numerical simulation of isotropic turbulence. We show that the orientation of the stress lags behind that of the strain rate, both at a single location and along trajectories. However, the timescale of the reorientation of the stress in these cases does not follow the expected dynamical scaling with length scale. To capture the proper dynamical scaling, we reformulate the energy flux between scales using the right Cauchy-Green strain tensor and the second Piola-Kirchhoff stress tensor. Our results highlight the key role played by the deformation of fluid elements in the physics of the energy cascade, and suggest that their irreversible deformation is a Lagrangian manifestation of the cascade's broken time-reversal symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Stress computation in displacement methods for two-material elastic media

The method of best fit strain tensors is extended to compute the stresses satisfying the conditions of equilibrium, compatibility, and constitutive relationships. It is assumed that the deflections at the mesh points have already been computed with acceptable accuracy. Results of examples presented show better accuracy than the usual procedure, in which equilibrium conditions are not enforced. Special emphasis is placed here upon two-material elastic media.

Salama, M.↗
DOE OSTI2023

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the $k−2L−a−\mathscr{C}$ and $k−ϕ−L−a−\mathscr{C}$ models by Morgan. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called “tilted rocket rig” inclined RT experiment and in simulation of a shock-accelerated localized patch of turbulence. Here it is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Residual lattice strain in quartzites as a potential palaeo-piezometer

SUMMARY If a crystal lattice is subjected to a stress, it becomes distorted and no longer represents the ideal crystal symmetry, and if the stress introduces defects such as dislocations, some of this distortion is preserved after the applied stress is removed. In this study, we investigate lattice distortion in quartz at the micron scale with synchrotron X-ray Laue diffraction. From Laue images the local deviatoric strain tensor is derived and corresponding stresses are calculated based on elastic properties. The method is applied to metasedimentary quartzites from the Bergell Alps that were deformed at conditions of greenschist facies metamorphism. The residual palaeostrain is represented in maps of the deviatoric strain tensor components and with deviatoric strain axis pole figures. Data suggest overall shortening perpendicular to the schistosity plane but with considerable asymmetry relative to foliation and lineation, probably attributed to simple shear. Crystallographic pole figures from Laue diffraction agree with neutron diffraction and EBSD measurements and display quartz c-axes girdle distributions with maxima also perpendicular to schistosity. The method shows promise to be used as a palaeo-piezometer to unravel the stress field during tectonic deformation.

58 GEOSCIENCES↗
NASA NTRS1977

Evaluation of the Tensor Polynomial and Hoffman strength theories for composite materials

The Hoffman theory and the Tensor Polynomial (Tsai-Wu) theory with the stress interaction term set equal to zero have been found to be preferred alternatives to the general Tensor Polynomial theory for predicting strength of filamentary composite laminae. These theories were used to predict failure of off-axis boron/epoxy and E-glass/epoxy test specimens and gave excellent agreement with available experimental results. A numerical experiment was also performed to estimate the errors for ten different composite systems under six different loadings. The maximum error in predicted failure loads among all cases was below 10 percent. These results suggest that the Hoffman failure theory and the Tensor Polynomial theory with the stress interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.

Narayanaswami, R.↗
NASA NTRS1992

Visualization of second order tensor fields and matrix data

We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order tensor fields.

Delmarcelle, Thierry↗
NASA NTRS2001

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Zhao, C. Y.↗
DOE OSTI2020

Viscometric flow of dense granular materials under controlled pressure and shear stress

This study examines the flow of dense granular materials under external shear stress and pressure using discrete element method simulations. In this method, the material is allowed to strain along all periodic directions and adapt its solid volume fraction in response to an imbalance between the internal state of stress and the external applied stress. By systematically varying the external shear stress and pressure, the steady rheological response is simulated for: (1) rate-independent quasi-static flow; and (2) rate-dependent inertial flow. The simulated flow is viscometric with non-negligible first and second normal stress differences. While both normal stress differences are negative in inertial flows, the first normal stress difference switches from negative to slightly positive, and second normal stress difference tends to zero in quasi-static flows. The first normal stress difference emerges from a lack of coaxiality between a second-rank contact fabric tensor and strain rate tensor in the flow plane, while the second normal stress difference is linked to an excess of contacts in the shear plane compared with the vorticity direction. A general rheological model of second order (in terms of strain rate tensor) is proposed to describe the two types of flow, and the model is calibrated for various values of interparticle friction from simulations on nearly monodisperse spheres. The model incorporates normal stress differences in both regimes of flow and provides a complete viscometric description of steady dense granular flows.

42 ENGINEERING↗
NASA NTRS2006

Anisotropic Developments for Homogeneous Shear Flows

The general decomposition of the spectral correlation tensor R(sub ij)(k) by Cambon et al. (J. Fluid Mech., 202, 295; J. Fluid Mech., 337, 303) into directional and polarization components is applied to the representation of R(sub ij)(k) by spherically averaged quantities. The decomposition splits the deviatoric part H(sub ij)(k) of the spherical average of R(sub ij)(k) into directional and polarization components H(sub ij)(sup e)(k) and H(sub ij)(sup z)(k). A self-consistent representation of the spectral tensor in the limit of weak anisotropy is constructed in terms of these spherically averaged quantities. The directional polarization components must be treated independently: models that attempt the same representation of the spectral tensor using the spherical average H(sub ij)(k) alone prove to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. The degree of anisotropy permitted by this theory is restricted by realizability requirements. Since these requirements will be less severe in a more accurate theory, a preliminary account is given of how to generalize the formalism of spherical averages to higher expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in tensorial spherical harmonics generated by irreducible representations of the spatial rotation group SO(exp 3). These expansions are considered in more detail in the special case of axial symmetry.

Cambon, Claude↗
NASA NTRS2002

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

Carlson, John R.↗
DOE OSTI2022

Ab initio calculations of third-order elastic coefficients

Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an “effective” third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. Additionally, we extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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.↗
DOE OSTI2020

Directional Cooling-Induced Fracturing Westerly Granite Test Results

Directional Cooling-Induced Fracturing (DCIF) experiments were conducted on a short, cylindrical sample of Westerly granite (diameter = 4 inches, height ~ 2 inches). Liquid nitrogen was poured in a copper cup attached to the top of the sample, and the resulting acoustic emissions (AEs) and temperature changes on the surface of the sample were monitored. The obtained AEs were used to determine the microcracking source locations and amplitude, and the associated moment tensors. Included in this submission is an animation of the AEs, a graphic displaying the temperature changes, and the measured data.

15 GEOTHERMAL ENERGY↗
NASA NTRS1993

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theoretically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.

Arnold, S. M.↗
NASA NTRS1993

Explicit robust schemes for implementation of general principal value-based constitutive models

The issue of developing effective and robust schemes to implement general hyperelastic constitutive models is addressed. To this end, special purpose functions are used to symbolically derive, evaluate, and automatically generate the associated FORTRAN code for the explicit forms of the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid for the entire deformation range. The analytical form of these explicit expressions is given here for the case in which the strain-energy potential is taken as a nonseparable polynomial function of the principle stretches.

Arnold, S. M.↗
DOE OSTI2023

Residual strain orientation in rolled titanium determined with synchrotron X-ray Laue microdiffraction

Previously, synchrotron X-ray Laue microdiffraction has been used to measure the magnitudes of residual strain in materials. Recently the method was advanced to determine the orientation of the strain ellipsoid and applied to naturally deformed quartzites; however, the deformation history of these quartzites is ambiguous due to their natural origin. Here, in this study, synchrotron X-ray Laue microdiffraction (µXRD) is used to measure the residual strain for the first time in a sample with known stress history, rolled titanium. A deviatoric strain tensor is calculated from each Laue diffraction image collected with two µXRD scans of a rolled titanium sheet in different sample orientations. The principal strain axes are calculated using an eigen decomposition of the deviatoric strain tensors. The results show that the principal axis of compression is aligned with the normal direction of the titanium sheet, and the principal axis of extension is aligned with the rolling direction. Pole figures are used to represent the 3D distribution of residual strain axes.

36 MATERIALS SCIENCE↗