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NASA NTRS1979

A fast, conservative algorithm for solving the transonic full-potential equation

A fast, fully implicit approximate factorization (AF) algorithm designed to solve the conservative transonic full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., 'rotated differencing'), and thereby greatly enhances the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line overrelaxation algorithms.

Holst, T. L.↗

NASA NTRS1982

Idealized dynamic grid computation of physical systems

The construction and utility of an idealized computational space for finite-difference computation of physical systems are considered. All computations are performed in tau space, which at any instant represents the dynamic grid of a subject physical system appropriately stretched into a uniform, orthogonal grid. A strain field model of physical system is described, including the sample computation of strain density fields. Dynamic grid generation using invariant-mapping is addressed, and the tau computational space is considered, including a grid dynamism constraint, a grid orthogonality constraint, and a grid smoothness constraint. The detailed tau computational space method is presented and illustrated with two sample problems.

Anyiwo, J. C.↗

NASA NTRS1987

A computational analysis of flow separation over five different airfoil geometries at high angles-of-attack

The flux splitting method of Van Leer (1982) and an implicit, upwind-biased, finite-volume scheme of Rumsey (1985) for solving the two-dimensional Reynolds-averaged Navier-Stokes equations were applied to analyze five airfoil geometries (the NACA 0012, 12-percent Joukowski, NACA 4412, NACA 65-015, and LS1-0417 sections), at high angles of attack. The effect of grid density and grid extent on the Strouhal number of the unsteady flow was computed, as well as the effect of variations in Mach number, Reynolds number, and angle of attack. It was found, that past an angle of attack of 20 deg, Strouhal numbers were independent of angle of attack (at a constant value of 0.115), agreeing well with the experimental findings of Tyler (1931).

Rumsey, Christopher L.↗

NASA NTRS1994

Probabilistic Simulation of Stress Concentration in Composite Laminates

A computational methodology is described to probabilistically simulate the stress concentration factors (SCF's) in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties, whereas the finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate SCF's, such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using is to simulate the SCF's in three different composite laminates. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the SCF's are influenced by local stiffness variables, by load eccentricities, and by initial stress fields.

Chamis, C. C.↗

NASA NTRS2001

Analyses for Debonding of Stitched Composite Sandwich Structures Using Improved Constitutive Models

A fracture mechanics analysis based on strain energy release rates is used to study the effect of stitching in bonded sandwich beam configurations. Finite elements are used to model the configurations. The stitches were modeled as discrete nonlinear spring elements with a compliance determined by experiment. The constitutive models were developed using the results of flatwise tension tests from sandwich material rather than monolithic material. The analyses show that increasing stitch stiffness, stitch density and debond length decrease strain energy release rates for a fixed applied load.

Glaessgen, E. H.↗

NASA NTRS2002

Finite Element Modeling of Deployment, and Foam Rigidization of Struts and Quarter Scale Shooting Star Experiment

Inflated cylindrical struts constructed of kapton polyimide film and rigidized with foam have considerable practical application and potential for use as components of inflatable concentrator assemblies, antenna structures and space power systems, Because of their importance, it is of great interest to characterize the dynamic behavior of these components and structures both experimentally and analytically. It is very helpful to take a building-block approach to modeling and understanding inflatable assemblies by first investigating in detail the behavior of the components such as the struts. The foam material used for rigidization of such cylinders has varying modulus, which is a function of different factors, such as density of the foam. Thus, the primary motivation of the tests and analytical modeling efforts was to determine and understand the response of foam-rigidized cylinders for different densities, sizes, and construction methods. In recent years, inflatable structures have been the subject of renewed interest for space applications such as communications antennae, solar thermal propulsion, and space solar power. A major advantage of using inflatable structures in space is that they are extremely lightweight. This makes inflatables a perfect match for solar thermal propulsion because of the low thrust levels available. An obvious second advantage is on-orbit deployability and subsequent space savings in launch configuration. It can be seen that inflatable cylindrical struts and torus are critical components of structural assemblies. In view of this importance, structural dynamic and static behaviors of typical rigidized polyimide struts are investigated in this paper. The paper will focus on the finite element models that were used to model the behavior of the complete solar collector structure, and the results that they provided, as compared to test data.

Larry Leigh, Jr.↗

NASA NTRS1994

Effect of density gradients in confined supersonic shear layers. Part 2: 3-D modes

The effect of basic flow density gradients on the supersonic wall modes were investigated in Part 1 of this analysis. In that investigation only the 2-D modes were studied. Tam and Hu investigated the 3-D modes in a confined vortex sheet and reported that the first 2-D Class A mode (A01) had the highest growth rate compared to all other 2-D and 3-D modes present in the vortex sheet for that particular set of flow patterns. They also showed that this result also held true for finite thickness shear layers with delta(sub w) less than 0.125. For free shear layers, Sandham and Reynolds showed that the 3-D K-H mode became the dominant mode for M(sub c) greater than 0.6. Jackson and Grosch investigated the effect of crossflow and obliqueness on the slow and fast odes present in a M(sub c) greater than 1 environment and showed that for certain combination of crossflow and wave angles the growth rates could be increased by up to a factor of 2 with respect to the 2-D case. The case studied here is a confined shear layer shown in Part 1. All solution procedures and basic low profiles are the same as in Part 1. The effect of density gradients on the 3-D modes present in the density ratios considered in Part 1 are investigated.

Peroomian, Oshin↗

NASA NTRS1974

Influence of ablation impurities on blunt body re-entry ionization

Electron density profiles which include the effect of an ablated sodium impurity were computed for the boundary layer on a blunt-nosed body re-entering the atmosphere at 7.62 km/sec. Profiles are computed from the nose to a distance of four diameters along the RAM C-payload. A finite-difference, laminar, nonequilibrium chemistry boundary-layer program was used. Comparison of theory with S-band diagnostic antenna results, electron concentration deduced from X- and C-band attenuation data, and Langmuir probe data at several different aft body locations show that agreement is good at high altitude. At the lower altitudes there is disagreement between theory and S-band antenna data where the apparent discrepancy is attributed to the three-body recombination rate constant used for deionization of sodium coupled with the effect of angle of attack.

Schexnayder, C. J., Jr.↗

NASA NTRS1978

Equation of state fits to the lower mantle and outer core

The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data. Homogeneous regions are found at radii between 5125 and 4825 km, 4600 and 3850 km, and 3200 and 2200 km. The lower mantle and outer core are inhomogeneous on the whole and are only homogeneous in the above local regions. Finite-strain and atomistic equations of state are fit to the homogeneous regions. The apparent convergence of the finite-strain relations is examined to judge their applicability to a given region. In some cases the observed pressure derivatives of the elastic moduli are used as additional constraints. The effect of minor deviations from adiabaticity on the extrapolations is also considered. An ensemble of zero-pressure values of the density and seismic velocities are found for these regions. The range of extrapolated values from these several approaches provides a measure of uncertainties involved.

Butler, R.↗

NASA NTRS1984

The laboratory simulation of unmagnetized supernova remnants Absence of a blast wave

Supernova remnants are experimentally simulated by irradiating spherical targets with eight-beam carbon dioxide laser in a chamber containing finite amounts of neutral gas, the gas being ionized by radiation from the hot target. The expansion velocities of the target plasmas are approximately the same as the expansion velocities of supernova ejecta and the experiment is successfully scaled to the case of a supernova remnant in an unmagnetized, low-density, interstellar medium. No sweep-up of the ambient plasma is detected, indicating that no hydrodynamic shock wave is formed to couple the target ejecta to the ambient gas. The experiment implies that if supernova ejecta couple to the interstellar medium, magnetic-field effects may be crucial to the physical description.

Borovsky, J. E.↗

NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗

NASA NTRS1994

A simulation study of radial expansion of an electron beam injected into an ionospheric plasma

Injections of nonrelativistic electron beams from a finite equipotential conductor into an ionospheric plasma have been simulated using a two-dimensional electrostatic particle code. The purpose of the study is to survey the simulation parameters for understanding the dependence of beam radius on physical variables. The conductor is charged to a high potential when the background plasma density is less than the beam density. Beam electrons attracted by the charged conductor are decelerated to zero velocity near the stagnation point, which is at a few Debye lengths from the conductor. The simulations suggest that the beam electrons at the stagnation point receive a large transverse kick and the beam expands radially thereafter. The buildup of beam electrons at the stagnation point produces a large electrostatic force responsible for the transverse kick. However, for the weak charging cases where the background plasma density is larger than the beam density, the radial expansion mechanism is different; the beam plasma instability is found to be responsible for the radial expansion. The simulations show that the electron beam radius for high spacecraft charging cases is of the order of the beam gyroradius, defined as the beam velocity divided by the gyrofrequency. In the weak charging cases, the beam radius is only a fraction of the beam gyroradius. The parameter survey indicates that the beam radius increases with beam density and decreases with magnetic field and beam velocity. The beam radius normalized by the beam gyroradius is found to scale according to the ratio of the beam electron Debye length to the ambient electron Debye length. The parameter dependence deduced would be useful for interpreting the beam radius and beam density of electron beam injection experiments conducted from rockets and the space shuttle.

Koga, J.↗

NASA NTRS2012

Functionally Graded Adhesives for Composite Joints

Adhesives with functionally graded material properties are being considered for use in adhesively bonded joints to reduce the peel stress concentrations located near adherend discontinuities. Several practical concerns impede the actual use of such adhesives. These include increased manufacturing complications, alterations to the grading due to adhesive flow during manufacturing, and whether changing the loading conditions significantly impact the effectiveness of the grading. An analytical study is conducted to address these three concerns. An enhanced joint finite element, which uses an analytical formulation to obtain exact shape functions, is used to model the joint. Furthermore, proof of concept testing is conducted to show the potential advantages of functionally graded adhesives. In this study, grading is achieved by strategically placing glass beads within the adhesive layer at different densities along the joint.

Stapleton, Scott E.↗

NASA NTRS2014

TBS (Trabecular Bone Score) Expands Understanding of Spaceflight Effects on the Lumbar Spine of Long Duration Astronauts

Background: Bone loss due to long-duration spaceflight has been characterized by both DXA and QCT serial scans. It is unclear if these spaceflight-induced changes in bone mineral density and structure result in increased fracture incidence. NASA astronauts currently fly on 5-6-month missions on the International Space Station (ISS) and at least one 12-month mission is planned. While NASA has measured areal BMD (by DXA) and volumetric BMD (by QCT), and has estimated hip strength (by finite element models of QCT data, no method has yet been used to examine bone microarchitecture from lumbar spine (LS). DXA scans are routinely performed pre- and post-flight on all ISS astronauts to follow BMD changes associated with space flight. Trabecular Bone Score (TBS) is a relatively new method that measures grey-scale-level texture information extracted from lumbar spine DXA images and correlates with 3D parameters of bone micro-architecture. We evaluated the ability of LS TBS to discriminate changes in astronauts who have flown on ISS missions and to determine if TBS can provide additional information compared to DXA. Methods: LS (L1-4) DXA scans from 51 astronauts (mean age, 47 +/- 4) were divided into 3 groups based on the exercise regimes performed while onboard the ISS. Pre-ARED (exercise using a load-limited resistive exercise device, <300lb), ARED (exercise with a high-load resistive exercise device, up to 600lb) and a Bisphos group (ARED exercise and a 70-mg alendronate tablet once a week before and during flight, starting 17 days before launch). DXA scans were performed and analyzed on a Hologic Discovery W using the same technician for the pre- and postflight scans. LSC for the LS in our laboratory is 0.025 g/cm2. TBS was performed at the Mercy Hospital, Cincinnati, Ohio on a similar Hologic computer. TBS precision was calculated from 16 comparable test subjects (0.0XX g/cm2). Data were preliminary analyzed using a paired, 2-tailed t-test for the difference between pre- and postflight means.

Sibonga, Jean D.↗

NASA NTRSDate not supplied

Overview of Ablative TPS Modeling at NASA Ames

Over the past decade, NASA has invested in efforts to build predictive thermal protection system (TPS) material models from the micro-scale to the macro-scale. To complement the mission design cycle process and reduce the need for extensive testing, NASA is developing modeling and simulation tools that enable characterizing material properties and response to hot plasma experienced during atmospheric entry. Traditional material response and ablation modeling tools, such as the heritage code FIAT, and its multidimensional siblings, TITAN and 3dFIAT, are being complemented with newly developed software such as Icarus and PATO. Both of these programs are three-dimensional, finite-volume solvers that use unstructured meshes and 21st century programming paradigms to allow for efficient parallel simulations. FIAT and Icarus are also used for TPS sizing purposes. Today, these traditional tools are being supplemented with computational materials models at the atomistic level. The scales of interest range from computational chemistry (Density Functional Theory [DFT]), to atomistic simulations (Molecular Dynamics [MD]), to the microscale with the Porous Microstructure Analysis (PuMA) software that was recently awarded the 2022 NASA Software of the Year award. Finally, thermo-structural modeling is also of interest to the TPS Materials branch and done using commercial tools such as MSC MARC, MENTAT, NASTRAN and PATRAN. The present talk will also link the use of these computational tools to current NASA missions and projects associated with challenging and complex vehicles entries/reentries.

materials modeling↗

NASA NTRS1981

Anomalous resistivity on auroral field lines

Consideration is given to a possible explanation for the one-dimensional anomalous resistivity and breakdown of runaway acceleration observed in the auroral zones. It is shown that under conditions existing along auroral field lines, where the cyclotron frequency is greater than the plasma frequency and density fluctuations exceed 0.25, trapping of a major portion of the electron distribution function by large-amplitude ion cyclotron waves can inhibit the free acceleration of runaways and act to violate the conservation of the first adiabatic invariant for electrons above a certain threshold velocity. Particle simulations combining the effects of finite ion cavities and pitch angle scattering at the anomalous Doppler resonance are then presented which demonstrate the formation of a runaway distribution upon the application of a constant dc field and the effects of the instability at the anomalous Doppler resonance in preventing it. The necessity for further large-scale macrophysics simulations to gain a fuller understanding of the total system dynamics is pointed out.

Rowland, H. L.↗

NASA NTRS1988

Sampling inhomogeneous turbulent fields

The reconstruction of an inhomogeneous random process from a finite number of discrete samples can be performed in terms of the Karhunen-Loeve (KL) expansion for that process. The n(th) eigenfunction has n - 1 zero crossings which are the sampling points for the inhomogeneous process. The rapid variation of the KL eigenfunctions makes it unnecessary to have a high density of sampling (or grid points) near the wall. However, this result should not be construed to indicate that with spectral simulations significantly fewer grid points are required with the KL expansion as compared to other orthogonal expansions. Moin and Moser (1989) have shown that the advantage of the KL expansion over Chebychev expansion rapidly diminishes when high percentage (say 90 percent) energy recovery is demanded.

Adrian, R. J.↗

NASA NTRS1990

A numerical method for phase-change problems

A highly accurate and efficient finite-difference method for phase-change problems with multiple moving boundaries of irregular shape is developed by employing a coordinate transformation that immobilizes moving boundaries and preserves the conservative forms of the original governing equations. The numerical method is first presented for one-dimensional phase-change problems (involving large density variation between phases, heat generation, and multiple moving boundaries) and then extended to solve two-dimensional problems (without change of densities between phases). Numerical solutions are obtained non-iteratively using an explicit treatment of the interfacial mass and energy balances and an implicit treatment of the temperature field equations. The accuracy and flexibility of the present numerical method are verified by solving some phase-change problems and comparing the results with existing analytical, semi-analytical and numerical solutions. Results indicate that one- and two-dimensional phase-change problems can be handled easily with excellent accuracies.

Kim, Charn-Jung↗