Search NASA⌕ Search

SEARCH · Search NASA

Results for “Constitutive models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32

Black Hole Mergers as Probes of Structure Formation

Intense structure formation and reionization occur at high redshift, yet there is currently little observational information about this very important epoch. Observations of gravitational waves from massive black hole (MBH) mergers can provide us with important clues about the formation of structures in the early universe. Past efforts have been limited to calculating merger rates using different models in which many assumptions are made about the specific values of physical parameters of the mergers, resulting in merger rate estimates that span a very wide range (0.1 - 104 mergers/year). Here we develop a semi-analytical, phenomenological model of MBH mergers that includes plausible combinations of several physical parameters, which we then turn around to determine how well observations with the Laser Interferometer Space Antenna (LISA) will be able to enhance our understanding of the universe during the critical z 5 - 30 structure formation era. We do this by generating synthetic LISA observable data (total BH mass, BH mass ratio, redshift, merger rates), which are then analyzed using a Markov Chain Monte Carlo method. This allows us to constrain the physical parameters of the mergers. We find that our methodology works well at estimating merger parameters, consistently giving results within 1- of the input parameter values. We also discover that the number of merger events is a key discriminant among models. This helps our method be robust against observational uncertainties. Our approach, which at this stage constitutes a proof of principle, can be readily extended to physical models and to more general problems in cosmology and gravitational wave astrophysics.

Alicea-Munoz, E.↗

Time Variable Gravity modeling for Precise Orbits Across the TOPEX/Poseidon, Jason-l and Jason-2 Missions

Modeling of the Time Variable Gravity (TVG) is believed to constitute one of the the largest remaining source of orbit error for altimeter satellite POD. The GSFC operational TVG model consists of forward modeling the atmospheric gravity using ECMWF 6-hour pressure data, a GRACE derived 20x20 annual field to account for changes in the hydrology and ocean water mass, and linear rates for C20, C30, C40, based on 17 years of SLR data analysis (IERS 2003) using the EIGEN-GL04S1 (a GRACE+Lageos-based geopotential solution). Although the GSFC Operational model can be applied from 1987, there may be long-term variations not captured by these linear models, and more importantly the linear models may not be consistent with more recent surface mass trends due to global climate change, We have evaluated the impact of TVG in two different wavs: (1) by using the more recent EIGEN-6S gravity model developed by the GFZ/GRGS tearm, which consists of annual, semi-annual and secular changes in the coefficients to 50x50 determined over 8(?) years of GRACE+Lageos+GOCE data (2003-200?): (2) Application of 4x4 solutions developed from a multi satellite SLR+DORIS solution based on GGM03S that span the period from 1993 to 2011. We have evaluated the recently released EIGEN6s static and time-varying gravity field for Jason-2 (J2). Jason-I (J1), and TOPEX/Posiedon (TP) Precise Orbit Determination (POD) spanning 1993-2011. Although EIGEN6s shows significant improvement for J2POD spanning 2008 - 2011, it also shows significant degradation for TP POD from 1992. The GSFC 4x4 time SLR+DORIS-based series spans 1993 to mid 2011, and shows promise for POD. We evaluate the performance of the different TVG models based on analysis of tracking data residuals use of independent data such as altimeter crossovers, and through analysis of differences with internally-generated and externally generated orbits.

Zelensky, Nikita P.↗

Elastic and Piezoelectric Properties of Boron Nitride Nanotube Composites: Finite Element Model - Part II

This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents finite element (FE) models to investigate the effective elastic and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall elastic and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for finite length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the finite element model to enable the modeling of multiple BNNTs in a polymer matrix.

Kim, H. Alicia↗

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗

Modeling of delamination damage evolution in laminated composites subjected to low velocity impact

This study examines the delamination evolution, under quasi-static conditions, of laminated polymeric composites with mechanically nonlinear resin rich interfaces. The constitutive behavior of the interface is represented by two models developed by Needleman and Tvegaard. These models assumed that the interfacial tractions, a function of only the interfacial displacement, will behave similarly to the interatomic forces generated during the interatomic seperation. The interface material's parameters control the load at which the delamination growth initiates and the final delamination size. A wide range of damage accumulation responses have been obtained by varying the model parameters. These results show that Tvergaard's model has been found to be better suited of the two models in predicting damage evolution for the configurations examined.

Lo, David C.↗

Calculations of lightning return stroke electric and magnetic fields above ground

A lightning return stroke model with which the two station electric and magnetic fields measured at ground level can be reproduced is used to compute fields at altitudes up to 10 km and at ranges from 20 m to 10 km. These calculations provide the first detailed estimates of the return strokes fields that are encountered by aircraft in flight. With the advent of modern aircraft utilizing low voltage digital electronics and reduced electromagnetic shielding by way of structures containing advanced composite materials, these calculations are of considerable practical interest. Further, since airborne electric and magnetic field measurements are presently being attempted, a comparison of the calculations presented with appropriate experimental data, when they are available, will constitute a test of the return stroke model.

Uman, M. A.↗

Technique for Calculating Solution Derivatives With Respect to Geometry Parameters in a CFD Code

A solution has been developed to the challenges of computation of derivatives with respect to geometry, which is not straightforward because these are not typically direct inputs to the computational fluid dynamics (CFD) solver. To overcome these issues, a procedure has been devised that can be used without having access to the mesh generator, while still being applicable to all types of meshes. The basic approach is inspired by the mesh motion algorithms used to deform the interior mesh nodes in a smooth manner when the surface nodes, for example, are in a fluid structure interaction problem. The general idea is to model the mesh edges and nodes as constituting a spring-mass system. Changes to boundary node locations are propagated to interior nodes by allowing them to assume their new equilibrium positions, for instance, one where the forces on each node are in balance. The main advantage of the technique is that it is independent of the volumetric mesh generator, and can be applied to structured, unstructured, single- and multi-block meshes. It essentially reduces the problem down to defining the surface mesh node derivatives with respect to the geometry parameters of interest. For analytical geometries, this is quite straightforward. In the more general case, one would need to be able to interrogate the underlying parametric CAD (computer aided design) model and to evaluate the derivatives either analytically, or by a finite difference technique. Because the technique is based on a partial differential equation (PDE), it is applicable not only to forward mode problems (where derivatives of all the output quantities are computed with respect to a single input), but it could also be extended to the adjoint problem, either by using an analytical adjoint of the PDE or a discrete analog.

Mathur, Sanjay↗

Prediction of Turbulent Diffusing Flows Using FUN3D

The FUN3D code was used to perform Reynolds-averaged Navier-Stokes (RANS) simulations to compute subsonic flow in an S-duct diffuser and transonic flow in a two-dimensional diffuser using the Speziale-Sarkar-Gatski/Launder-Rodi-Reece (SSG/LRR) Reynolds stress model (RSM). For comparison purposes, additional simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST) turbulence models. Each model was run with and without the quadratic constitutive relation (QCR) for computing the turbulent stresses. It was shown that the simulations that utilized the RSM had better overall predictions of the diffusive flow fields compared to the simulations that utilized the one and two equation turbulence models.

Inlet Distortion↗

Prediction of Turbulent Diffusing Flows Using FUN3D

The FUN3D code was used to perform Reynolds-averaged Navier-Stokes (RANS) simulations to compute subsonic flow in an S-duct diffuser and transonic flow in a two-dimensional diffuser using the Speziale-Sarkar-Gatski/Launder-Rodi-Reece (SSG/LRR) Reynolds stress model (RSM). For comparison purposes, additional simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST) turbulence models. Each model was run with and without the quadratic constitutive relation (QCR) for computing the turbulent stresses. It was shown that the simulations that utilized the RSM had better overall predictions of the diffusive flow fields compared to the simulations that utilized the one and two equation turbulence models.

Inlet Distortion↗

Analysis of metal-matrix composite structures. I - Micromechanics constitutive theory. II - Laminate analyses

The micromechanical constitutive theory is used to examine the nonlinear behavior of continuous-fiber-reinforced metal-matrix composite structures. Effective lamina constitutive relations based on the Abouli micromechanics theory are presented. The inelastic matrix behavior is modeled by the unified viscoplasticity theory of Bodner and Partom. The laminate constitutive relations are incorporated into a first-order deformation plate theory. The resulting boundary value problem is solved by utilizing the finite element method. Attention is also given to computational aspects of the numerical solution, including the temporal integration of the inelastic strains and the spatial integration of bending moments. Numerical results the nonlinear response of metal matrix composites subjected to extensional and bending loads are presented.

Arenburg, R. T.↗

The Z3 model of Saturns magnetic field and the Pioneer 11 vector helium magnetometer observations

Magnetic field observations obtained by the Pioneer 11 vector helium magnetometer are compared with the Z(sub 3) model magnetic field. These Pioneer 11 observations, obtained at close-in radial distances, constitute an important and independent test of the Z(sub 3) zonal harmonic model, which was derived from Voyager 1 and Voyager 2 fluxgate magnetometer observations. Differences between the Pioneer 11 magnetometer and the Z(sub 3) model field are found to be small (approximately 1%) and quantitatively consistent with the expected instrumental accuracy. A detailed examination of these differences in spacecraft payload coordinates shows that they are uniquely associated with the instrument frame of reference and operation. A much improved fit to the Pioneer 11 observations is obtained by rotation of the instrument coordinate system about the spacecraft spin axis by 1.4 degree. With this adjustment, possibly associated with an instrumental phase lag or roll attitude error, the Pioneer 11 vector helium magnetometer observations are fully consistent with the Voyager Z(sub 3) model.

Connerney, J. E. P.↗

The Z3 model of Saturn's magnetic field and the Pioneer 11 vector helium magnetometer observations

Magnetic field observations obtained by the Pioneer 11 vector helium magnetometer are compared with the Z(sub 3) model magnetic field. These Pioneer 11 observations, obtained at close-in radial distances, constitute an important and independent test of the Z(sub 3) zonal harmonic model, which was derived from Voyager 1 and Voyager 2 fluxgate magnetometer observations. Differences between the Pioneer 11 magnetometer and the Z(sub 3) model field are found to be small (approximately 1 percent) and quantitatively consistent with the expected instrumental accuracy. A detailed examination of these differences in spacecraft payload coordinates shows that they are uniquely associated with the instrument frame of reference and operation. A much improved fit to the Pioneer 11 observations is obtained by rotation of the instrument coordinate system about the spacecraft spin axis by 1.4 degree. With this adjustment, possibly associated with an instrumental phase lag or roll attitude error, the Pioneer 11 vector helium magnetometer observations are fully consistent with the Voyager Z(sub 3) model.

Connerney, J. E. P.↗

An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials

A thermodynamically consistent damage model for the simulation of progressive delamination under variable mode ratio is presented. The model is formulated in the context of the Damage Mechanics (DM). The constitutive equations that result from the variation of the free energy with damage are used to model the initiation and propagation of delamination. A new delamination initiation criterion is developed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. Interfacial penetration of two adjacent layers after complete decohesion is prevented by the formulation of the free energy. The model is implemented into the commercial finite element code ABAQUS by means of a user-written decohesion element. Finally, the numerical predictions given by the model are compared with experimental results.

Turon, Albert↗

A study of the compatibility of an existing CFD package with a broader class of material constitutions

The flexibility of the PHOENICS computational fluid dynamics package was assessed along two general avenues; parallel modeling and analog modeling. In parallel modeling the dependent and independent variables retain their identity within some scaling factors, even though the boundary conditions and especially the constitutive relations do not correspond to any realistic fluid dynamic situation. PHOENICS was used to generate a CFD model that should exhibit the physical anomalies of a granular medium and permit reasonable similarity with boundary conditions typical to membrane or porous piston loading. A considerable portion of the study was spent prying into the existing code with a prejudice toward rate type and disarming any inherent fluid behavior. The final stages of the study were directed at the more specific problem of multiaxis loading of cylindrical geometry with a concern for the appearance of bulging, cross slab shear failure modes.

French, K. W., Jr.↗

Steady flow of a non-Newtonian fluid through a contraction

A steady-state analysis is conducted to examine the basic flow structure of a non-Newtonian fluid in a domain including an inflow region, a contraction region, and an outflow region. A Cartesian grid system is used throughout the entire flow domain, including the contraction region, thus creating an irregular grid cell structure adjacent to the curved boundary. At node points adjacent to the curved boundary symmetry conditions are derived for the different flow variables in order to solve the governing difference equations. Attention is given to the motion and non-Newtonian constitutive equations, the boundary conditions, the numerical modeling of the non-Newtonian equations, the stream function contour lines for the non-Newtonian fluid, the vorticity contour lines for the non-Newtonian fluid, the velocity profile across the contraction, and the shear stress contour lines for the non-Newtonian fluid.

Gatski, T. B.↗

Crater modification by gravity - A mechanical analysis of slumping

An analysis of the stability of a crater from a mechanical point of view indicates that the observed slumping of lunar craters requires a perfectly plastic constitutive relation for the lunar surface rock. The angle of internal friction of this material must be less than a few degrees. The evidence for a perfectly plastic constitutive relation is described, and a simplified model of a crater in a perfectly plastic medium is used to investigate the nature of its collapse. Crater stability is found to depend principally upon a dimensionless parameter equal to the product of the density, acceleration of gravity, and depth divided by the yield strength. Criteria for stability, 'slope failures', and 'floor failures' are reported.

Melosh, H. J.↗