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NASA NTRS1999

Turbulence Model Comparisons and Reynolds Number Effects Over a High-Speed Aircraft at Transonic Speeds

This paper gives the results of a grid study, a turbulence model study, and a Reynolds number effect study for transonic flows over a high-speed aircraft using the thin-layer, upwind, Navier-Stokes CFL3D code. The four turbulence models evaluated are the algebraic Baldwin-Lomax model with the Degani-Schiff modifications, the one-equation Baldwin-Barth model, the one-equation Spalart-Allmaras model, and Menter's two-equation Shear-Stress-Transport (SST) model. The flow conditions, which correspond to tests performed in the NASA Langley National Transonic Facility (NTF), are a Mach number of 0.90 and a Reynolds number of 30 million based on chord for a range of angle-of-attacks (1 degree to 10 degrees). For the Reynolds number effect study, Reynolds numbers of 10 and 80 million based on chord were also evaluated. Computed forces and surface pressures compare reasonably well with the experimental data for all four of the turbulence models. The Baldwin-Lomax model with the Degani-Schiff modifications and the one-equation Baldwin-Barth model show the best agreement with experiment overall. The Reynolds number effects are evaluated using the Baldwin-Lomax with the Degani-Schiff modifications and the Baldwin-Barth turbulence models. Five angles-of-attack were evaluated for the Reynolds number effect study at three different Reynolds numbers. More work is needed to determine the ability of CFL3D to accurately predict Reynolds number effects.

Rivers, Melissa B.↗

NASA NTRS1978

Mantle convection pattern and subcrustal stress field under Asia

Satellite tracking and surface gravity data are used to model the subcrustal stress fields in the terrestrial mantle beneath Asia; the results permit interpretation of the tectonic and seismic systems in China. The east and west China blocks, together with five seismic zones, are identified and related to metallogenic domains on the Chinese mainland. In addition, it is shown that the subcrustal stresses beneath China are arranged perpendicularly to the major fault systems and seismic belts. Stress calculations indicate a notable zone of compression in north China, associated with the Shansi Graben, the Linfen Basin Systems and, possibly, the high seismicity of the region.

Liu, H.-S.↗

NASA NTRS2017

The Implications of Tides on the Mimas Ocean Hypothesis

We investigate whether a present-day global ocean within Mimas is compatible with the lack of tectonic activity on its surface by computing tidal stresses for ocean-bearing interior structure models derived from observed librations. We find that, for the suite of compatible rheological models, peak surface tidal stresses caused by Mimas' high eccentricity would range from a factor of 2 smaller to an order of magnitude larger than those on tidally active Europa. Thermal stresses from a freezing ocean, or a past higher eccentricity, would enhance present-day tidal stresses, exceeding the magnitudes associated with Europa's ubiquitous tidally driven fractures and, in some cases, the failure strength of ice in laboratory studies. Therefore, in order for Mimas to have an ocean, its ice shell cannot fail at the stress values implied for Europa. Furthermore, if Mimas' ocean is freezing out, the ice shell must also be able to withstand thermal stresses that could be an order of magnitude higher than the failure strength of laboratory ice samples. In light of these challenges, we consider an ocean-free Mimas to be the most straightforward model, best supported by our tidal stress analysis.

Rhoden, Alyssa Rose↗

NASA NTRS1983

Subsurface stress evaluations under rolling/sliding contacts

A computer model has been developed for evaluating the subsurface stresses incurred within rolling/sliding (elastic) contacts. The model involves first defining the stress tensor at any point (x, y, or z) beneath the surface in terms of the surface stresses. The stress tensors are analyzed to determine the maximum shear stresses and stress reversals. As a result of computations with the model, several observations were made. For example, the maximum reversing shear stresses are on the plane of the orthogonal shear stress. Further, the magnitude of these stresses is not altered by friction. However, under very high friction (typical of dry contact) surface stresses can dominate over subsurface stresses.

Kannel, J. W.↗

NASA NTRS2015

Impact and Penetration of Thin Aluminum 2024 Flat Panels at Oblique Angles of Incidence

The U.S. Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) are actively involved in improving the predictive capabilities of transient finite element computational methods for application to safety issues involving unintended impacts on aircraft and aircraft engine structures. One aspect of this work involves the development of an improved deformation and failure model for metallic materials, known as the Tabulated Johnson-Cook model, or MAT224, which has been implemented in the LS-DYNA commercial transient finite element analysis code (LSTC Corp., Livermore, CA) (Ref. 1). In this model the yield stress is a function of strain, strain rate and temperature and the plastic failure strain is a function of the state of stress, temperature and strain rate. The failure criterion is based on the accumulation of plastic strain in an element. The model also incorporates a regularization scheme to account for the dependency of plastic failure strain on mesh size. For a given material the model requires a significant amount of testing to determine the yield stress and failure strain as a function of the three-dimensional state of stress, strain rate and temperature. In addition, experiments are required to validate the model. Currently the model has been developed for Aluminum 2024 and validated against a series of ballistic impact tests on flat plates of various thicknesses (Refs. 1 to 3). Full development of the model for Titanium 6Al-4V is being completed, and mechanical testing for Inconel 718 has begun. The validation testing for the models involves ballistic impact tests using cylindrical projectiles impacting flat plates at a normal incidence (Ref. 2). By varying the thickness of the plates, different stress states and resulting failure modes are induced, providing a range of conditions over which the model can be validated. The objective of the study reported here was to provide experimental data to evaluate the model under more extreme conditions, using a projectile with a more complex shape and sharp contacts, impacting flat panels at oblique angles of incidence.

Ruggeri, Charles R.↗

NASA NTRS1984

A critical assessment of viscous models of trench topography and corner flow

Stresses for Newtonian viscous flow in a simple geometry (e.g., corner flow, bending flow) are obtained in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/R(2); for a step function velocity, stress goes as 1/R; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/R singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries. Topography and seismicity data from northern Hoshu, Japan, were used to construct a finite element model, with flow assumed tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography and gravity anomalies. There is poor agreement. Purely viscous models of subducting slables with specified velocity boundary conditions do not predict normal stress patterns compatible with observed topography and gravity. Elasticity and plasticity appear to be important for the subduction process.

Zhang, J.↗

NASA NTRS1985

A critical assessment of viscous models of trench topography and corner flow

Zhang, J.↗

NASA NTRS1992

A differential CDM model for fatigue of unidirectional metal matrix composites

A multiaxial, isothermal, continuum damage mechanics (CDM) model for fatigue of a unidirectional metal matrix composite volume element is presented. The model is phenomenological, stress based, and assumes a single scalar internal damage variable, the evolution of which is anisotropic. The development of the fatigue damage model, (i.e., evolutionary law) is based on the definition of an initially transversely isotropic fatigue limit surface, a static fracture surface, and a normalized stress amplitude function. The anisotropy of these surfaces and function, and therefore the model, is defined through physically meaningful invariants reflecting the local stress and material orientation. This transversely isotropic model is shown, when taken to it's isotropic limit, to directly simplify to a previously developed and validated isotropic fatigue continuum damage model. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation in attempting to characterize a class of composite materials, and (2) the capability of the formulation in predicting anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Also, specific material parameters representing an initial characterization of the composite system SiC/Ti 15-3 and the matrix material (Ti 15-3) are reported.

Arnold, S. M.↗

NASA NTRS2004

Stressed Oxidation Life Prediction for C/SiC Composites

The residual strength and life of C/SiC is dominated by carbon interface and fiber oxidation if seal coat and matrix cracks are open to allow oxygen ingress. Crack opening is determined by the combination of thermal, mechanical and thermal expansion mismatch induced stresses. When cracks are open, life can be predicted by simple oxidation based models with reaction controlled kinetics at low temperature, and by gas phase diffusion controlled kinetics at high temperatures. Key life governing variables in these models include temperature, stress, initial strength, oxygen partial pressure, and total pressure. These models are described in this paper.

Levine, Stanley R.↗

NASA NTRS2017

Plume-Surface Interaction Modeling for a Human-Scale Mars Lander

Landing vehicles impart thermal and strain energy onto the landing site from the retrorocket exhaust. Depending on the design of the vehicle, the energy may be great enough to cause spallation at the landing site. This damage may be minor and repairable in the case of landing on a terrestrial landing pad. For missions to other planetary bodies, the spallation may cause the landing site to become uneven and unstable, as well as damage. Simulating this phenomenon in a laboratory or computationally would require a significant amount of time and other resources. These resources typically are not available during the design phase of a mission. This paper presents a computationally-efficient model for the temperature and stress distributions that arise during landing. These quantities can be used along with existing failure criteria, such as the Hoek-Brown criterion for geological materials, to quickly determine whether spallation will occur. The stress and temperature distributions at the landing site are inherently 3D; however, there is a plane of symmetry and in that plane the distributions are 2D. Both quantities are modeled using series solutions to their governing partial differential equations (PDEs). The stress is modeled using the Airy stress potential function and its governing PDE is the biharmonic equation. The temperature is governed by Fourier's law. The models assume that stress due to gravity can be neglected, the points in the plane do not accelerate, and that the material properties are constant.

Hart, Kenneth↗

NASA NTRS1991

Modeling hypersonic boundary-layer flows with second-moment closure

An ongoing research effort designed to apply the best possible second-moment-closure model to simulate complex hypersonic flows is presented. The baseline model under consideration is the Launder-Reece-Rodi Reynolds stress transport turbulence model. Two add-ons accounting for wall effects, namely, the Launder-Shima low-Reynolds-number model and the compressible wall-function technique, are tested. Results are reported for flow over a flat plate, both adiabatic-wall and cooled-wall cases. It has been found that further improvements of the existing models are necessary to achieve accurate prediction in high Mach number flow range.

Huang, P. George↗

NASA NTRS1994

Modeling of Wall-Bounded Complex Flows and Free Shear Flows

Various wall-bounded flows with complex geometries and free shear flows have been studied with a newly developed realizable Reynolds stress algebraic equation model. The model development is based on the invariant theory in continuum mechanics. This theory enables us to formulate a general constitutive relation for the Reynolds stresses. Pope was the first to introduce this kind of constitutive relation to turbulence modeling. In our study, realizability is imposed on the truncated constitutive relation to determine the coefficients so that, unlike the standard k-E eddy viscosity model, the present model will not produce negative normal stresses in any situations of rapid distortion. The calculations based on the present model have shown an encouraging success in modeling complex turbulent flows.

Shih, Tsan-Hsing↗

NASA NTRS1990

A phenomenological model of coating/substrate adhesion and interfacial bimetallic peeling stress in composite mirrors

Adhesion and interfacial stress between metal films and structural composite material substrates is discussed. A theoretical and conceptual basis for selecting coating materials for composite mirror substrates is described. A phenomenological model that interrelates cohesive tensile strength of thin film coatings and interfacial peeling stresses is presented. The model serves as a basis in determining gradiated materials response and compatibility of composite substrate and coating combinations. Parametric evaluation of material properties and geometrical factors such as coating thickness are used to determine the threshold stress levels for maintaining adhesion at the different interfaces.

Mcelroy, Paul M.↗

NASA NTRS1992

Experimental, physical and numerical modeling of lunar regolith and lunar regolith structures

An extensive series of laboratory strength and deformation experiments have been performed on a lunar regolith simulant. Results of these experiments are compared to results from experiments on real lunar regolith from the Apollo and Luna missions to illustrate the suitability of this material in capturing the engineering properties lunar regolith. In addition, these results are used to calibrate a constitutive model used to describe its stress-strain behavior. This model, in conjunction with numerical analysis techniques, is used to predict the response i.e. material parameters) of lunar simulant under 1/6-g and low confining stress conditions. These tools are also used to predict the displacement response of a lunar soil embankment structure used to cover a first generation human habitat module, which might be used to accommodate the first astronauts revisiting the moon. These predictions are compared to physical models of this structure, which are tested in a geotechnical centrifuge in order to satisfy scaling relationships between prototype and model.

Perkins, Steven W.↗

NASA NTRS2006

Second Moment Closure Near the Two-component Limit

The purpose of this paper is to explore some wider implications of the two-component limit for both single point turbulence models and spectral closure theories. Although the two-component limit arises most naturally in inhomogeneous problems like wall-bounded turbulence, the analysis will be restricted to homogeneous turbulence. But since homogeneous turbulence is the crucial case for realizability, the conclusions will nevertheless be applicable to modeling. Th essential point of our argument is that whereas the evolution of the stochastic velocity field is Markovian because it is governed by the Navier-Stokes equations, the exact stress evolution equation is not Markovian because it is unclosed. This property of moment evolution has been stressed by Kraichnan (1959). We will show that modeling stress evolution at the two-component limit with a closure that is Markovian in the stresses alone leads to basic inconsistencies in single-point modeling and, perhaps surprisingly, in spectral modes as well.

Rubinstein, Robert↗

NASA NTRS1985

A study of the second and third order closure models of turbulence for prediction of separated shear flows

The hybrid model of the Reynolds-stress turbulence closure is tested for the computation of the flows over a step and disk. Here it is attempted to improve the redistributive action of the turbulence energy among the Reynolds stresses. By evaluating the existing models for the pressure-strain correlation, better coefficients are obtained for the prediction of separating shear flows. Furthermore, the diffusion rate of the Reynolds stresses is reevaluated adopting several algebraic correlations for the triple-velocity products. The models of Cormack et al., Daly-Harlow, Hanjalic-Launder, and Shir were tested for the reattaching shear flows. It was generally observed that all these algebraic models give considerably low values of the triple-velocity products. This is attributed to the fact that none of the algebraic models can take the convective effect of the triple-velocity products into account in the separating shear flows, thus resulting in much lower diffusion rate than Reynolds stresses. In order to improve the evaluation of these quantities correction factors are introduced based on the comparison with some experimental data.

Amano, R. S.↗

NASA NTRS1990

A macro-micromechanics analysis of a notched metal matrix composite

A macro-micromechanics analysis was formulated to determine the matrix and fiber behavior near the notch tip in a center-notched metal matrix composite. Results are presented for a boron/aluminum monolayer. The macro-level analysis models the entire notched specimen using a three dimensional finite element program which uses the vanishing-fiber-diameter model to model the elastic-plastic behavior of the matrix and the elastic behavior of the fiber. The micro-behavior is analyzed using a Discrete Fiber-Matrix (DFM) model containing one fabric and the surrounding matrix. The dimensions of the DFM model were determined by the ply thickness and the fiber volume fraction and corresponded to the size of the notch-tip element in the macro-level analysis. The boundary conditions applied to the DFM model were determined from the macro-level analysis. Stress components within the DFM model were calculated and stress distributions are presented along selected planes and surfaces within the DFM model, including the fiber-matrix interface. Yielding in the matrix was examined at the notch tip in both the macro- and micro-level analyses. The DFM model predicted higher stresses (24 percent) in the fiber compared to the global analysis. In the notch-tip element, the interface stresses indicated that a multi-axial criterion may be required to predict interfacial failure. The DFM analysis predicted yielding to initiate in the notch-tip element at a stress level 28 percent lower than predicted by the global analysis.

Bigelow, C. A.↗

NASA NTRS1983

Bellows flow-induced vibrations

The bellows flow excitation mechanism and results of comprehensive test program are summarized. The analytical model for predicting bellows flow induced stress is refined. The model includes the effects of an upstream elbow, arbitrary geometry, and multiple piles. A refined computer code for predicting flow induced stress is described which allows life prediction if a material S-N diagram is available.

Tygielski, P. J.↗