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NASA NTRS2017

Assessment of the Gaussian Covariance Approximation over an Earth-Asteroid Encounter Period

In assessing the risk an asteroid may pose to the Earth, the asteroids state is often predicted for many years, often decades. Only by accounting for the asteroids initial state uncertainty can a measure of the risk be calculated. With the asteroids state uncertainty growing as a function of the initial velocity uncertainty, orbit velocity at the last state update, and the time from the last update to the epoch of interest, the asteroids position uncertainties can grow to many times the size of the Earth when propagated to the encounter risk corridor. This paper examines the merits of propagating the asteroids state covariance as an analytical matrix. The results of this study help to bound the efficacy of applying different metrics for assessing the risk an asteroid poses to the Earth. Additionally, this work identifies a criterion for when different covariance propagation methods are needed to continue predictions after an Earth-encounter period.

planetary defense↗

NASA NTRS2017

Assessment of the Gaussian Covariance Approximation over an Earth-Asteroid Encounter Period

uncertainty characterization↗

NASA NTRS1973

Stress wave calculations in composite plates using the fast Fourier transform.

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Moon, F. C.↗

NASA NTRS1977

Implicit approximate-factorization schemes for the efficient solution of steady transonic flow problems

Implicit approximate-factorization algorithms (AF) are developed for the solution of steady-state transonic flow problems. The performance of the AF solution method is evaluated relative to that of the standard solution method for transonic flow problems, successive line over-relaxation (SLOR). Both methods are applied to the solution of the nonlinear, two-dimensional transonic small-disturbance equation. Results indicate that the AF method requires substantially less computer time than SLOR to solve the nonlinear finite-difference matrix equation for a transonic flow field. This increase in computational efficiency is achieved with no appreciable increase in computer storage or coding complexity.

Ballhaus, W. F.↗

NASA NTRS1992

LDEF materials: An overview of the interim findings

The flight and retrieval of the National Aeronautics and Space Administration's Long Duration Exposure Facility (LDEF) provided an opportunity for the study of the low-Earth orbit (LEO) environment and long-duration space environmental effect (SEE) on materials that are unparalleled in the history of the U.S. space program. The 5.8-year flight of LDEF greatly enhanced the potential value of materials data from LDEF to the international SEE community, compared to that of the original 1-year flight plan. The remarkable flight attitude stability of LDEF enables specific analyses of various individual and combined effects of LEO environmental parameters on identical materials of the same space vehicle. NASA recognized the potential by forming the LDEF Space Environmental Effects on Materials Special Investigation Group (MSIG) to address the greatly expanded materials and LEO space environment parameter analysis opportunities available in the LDEF structure, experiment trays, and corollary measurements, so that the combined value of all LDEF materials data to current and future space missions will be assessed and documented. This paper provides an overview of the interim LDEF materials findings of the Principal Investigators and the Materials Special Investigation Group. These revelations are based on observations of LEO environmental effects on materials made in-space during LDEF retrieval and during LDEF tray deintegration at the Kennedy Space Center, and on findings of approximately 1.5 years of laboratory analyses of LDEF materials by the LDEF materials scientists. These findings were extensively reviewed and discussed at the MSIG-sponsored LDEF Materials Workshop '91. The results are presented in a format which categorizes the revelations as 'clear findings' or 'confusing/unexplained findings' and resultant needs for new space materials developments and ground simulation testing/analytical modeling in seven categories: environmental parameters and data bases; LDEF contamination; thermal control coatings and protective treatments; polymers and films; polymer-matrix composites; metals, ceramics, and optical materials; and systems-related materials. General outlines of findings of the other LDEF Special Investigation Groups (Ionizing Radiation, Meteoroid and Debris, and Systems) are also included. The utilization of LDEF materials data for future low-earth orbit missions is also discussed, concentrating on Space Station Freedom. Some directions for continuing studies of LDEF materials are outlined. In general, the LDEF data is remarkable consistent; LDEF will provide a 'benchmark' for materials design data bases for satellites in low-Earth orbit. Some materials were identified to be encouragingly resistant to LEO SEE for 5.8-years; other 'space qualified' materials displayed significant environmental degradation. Molecular contamination was widespread; LDEF offers an unprecedented opportunity to provide a unified perspective of unmanned LEO spacecraft contamination mechanisms. New material development requirements for long-term LEO missions have been identified and current ground simulation testing methods/data for new, durable materials concepts can be validated with LDEF results. LDEF findings are already being integrated into the design of Space Station Freedom.

Stein, Bland A.↗

NASA NTRS1993

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Walker, Kevin P.↗

NASA NTRS1995

Numerical Simulations of High Enthalpy Pulse Facilities

Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.

Wilson, Gregory J.↗

NASA NTRS2020

Ultrasonic Lamb Wave Inspection of Composite Defects

Composites have been extensively used in aerospace engineering due to their advantages of light weight, high strength, and engineering design flexibility. Manufacturing defects such as wrinkle and porosity can affect the performance of the composites and may lead to failure in the end, while damage such as delamination, fiber fraction, and matrix cracking can directly cause failure of the composites. In this paper, a Lamb wave based nonintrusive nondestructive evaluation system, which employs piezoelectric transducer for actuation and scanning laser Doppler vibrometer for wavefield sensing, is presented for typical composite defect and damage inspection and evaluation. Two composite panels with different geometry (flat or curved) and with various embedded defects (wrinkle and delamination) are inspected using the nonintrusive Lamb wave system. Both the wrinkles and delamination are detected from the wavefield and approximately quantified through wavefield imaging methods.

Wrinkles↗

NASA NTRS1990

Effect of atmospherics on beamforming accuracy

Two mathematical representations of noise due to atmospheric turbulence are presented. These representations are derived and used in computer simulations of the Bartlett Estimate implementation of beamforming. Beamforming is an array processing technique employing an array of acoustic sensors used to determine the bearing of an acoustic source. Atmospheric wind conditions introduce noise into the beamformer output. Consequently, the accuracy of the process is degraded and the bearing of the acoustic source is falsely indicated or impossible to determine. The two representations of noise presented here are intended to quantify the effects of mean wind passing over the array of sensors and to correct for these effects. The first noise model is an idealized case. The effect of the mean wind is incorporated as a change in the propagation velocity of the acoustic wave. This yields an effective phase shift applied to each term of the spatial correlation matrix in the Bartlett Estimate. The resultant error caused by this model can be corrected in closed form in the beamforming algorithm. The second noise model acts to change the true direction of propagation at the beginning of the beamforming process. A closed form correction for this model is not available. Efforts to derive effective means to reduce the contributions of the noise have not been successful. In either case, the maximum error introduced by the wind is a beam shift of approximately three degrees. That is, the bearing of the acoustic source is indicated at a point a few degrees from the true bearing location. These effects are not quite as pronounced as those seen in experimental results. Sidelobes are false indications of acoustic sources in the beamformer output away from the true bearing angle. The sidelobes that are observed in experimental results are not caused by these noise models. The effects of mean wind passing over the sensor array as modeled here do not alter the beamformer output as significantly as expected.

Alexander, Richard M.↗

NASA NTRS1985

Fracture and crack growth in orthotropic laminates

A mathematical model based on the classical shear-lag assumptions is used to study the residual strength and fracture behavior of composite laminates with symmetrically placed buffer strips. The laminate is loaded by a uniform remote longitudinal tensile strain and has initial damage in the form of a transverse crack in the parent laminate between buffer strips. The crack growth behavior as a function of material properties, number of buffer-strip plies, spacing, width of buffer strips, longitudinal matrix splitting, and debonding at the interface is studied. Buffer-strip laminates are shown to arrest fracture and increase the residual strengths significantly over those of one material laminates, with S-glass being a more effective buffer strip material than Kevlar in increasing the damage tolerance of graphite/epoxy panels. For a typical graphite/epoxy laminate with S-glass buffer-strips, the residual strength is about 2.4 times the residual strength of an all graphite/epoxy panel with the same crack length. Approximately 50% of this increase is due to the S-glass/epoxy buffer-strips, 40% due to longitudinal splitting of the buffer strip interface and 10% due to bonding.

Goree, James G.↗

NASA NTRS1991

Superalloy for high-temperature hydrogen environmental applications

A nickel-based superalloy is provided which is resistant to deterioration in hydrogen at high operating temperatures and pressures, and which thus can be used in hydrogen-fueled spacecraft such as the Space Shuttle. The superalloy is characterized by a two-phase microstructure and consists of a gamma-prime precipitated phase in a gamma matrix. The gamma matrix phase is a primary solid solution and the gamma precipitated phase will be an intermetallic compound of the type A.sub.3 B, such as nickel aluminide or titanide. Both phases are coherent, ordered, and compatible, and thus will retain most of their strength at elevated temperatures. The alloy consists essentially of (by weight): Ni 50-60%, Cr 10-20%, Al 2-6%, Co 2-5%, Ti 3-8%, W 5-12%, Mo 5-10%, Nb 1-3%, wherein the ratio W/MO is approximately equal to 1, and Ti/Al ranges from about 1 to about 2.

McKannan, Eugene C.↗

NASA NTRS1980

Catalytic combustion of heavy partially-vaporized fuels

An experimental program to demonstrate efficient catalytic combustion of fuel-lean and fuel-rich mixtures of residual fuel and air, and to assess the influence of incomplete fuel vaporization on the performance of a catalytic reactor is being conducted. A 7.5-cm diameter catalytic reactor was designed and will be tested over a matrix of conditions representative of a gas turbine combustor inlet. For each of three test phases, two series of tests with a uniform but poorly vaporized (less than 50 percent) mixture of No. 6 fuel oil and air will be performed. In the first series, the non-vaporized fuel will be contained in a spray of droplets with a Sauter Mean Diameter (SMD) less than 30 microns. In the second series, the non-vaporized fuel will be characterized by a spray SMD approximately equal to 100 microns. The designs of the fuel injection system and the catalytic reactor are described in this paper.

Rosfjord, T. J.↗

NASA NTRS1989

Further Improvements to Nozzle Boundary Layer Calculations in BLIMPJ

Further improvements made to advance the current Boundary Layer Integral Matrix Procedure - Version J (BLIMPJ) containing previously modeled simplified calculation methods by accounting for condensed phase, thick boundary layer and free stream turbulence effects are discussed. The condensed phase effects were included through species composition effect considered via input to the code and through particle damping effect considered via a turbulence model. The thrust loss calculation procedure for thick boundary layer effects was improved and the optimization of net thrust with respect to nozzle length was performed. The effects of free stream turbulence were approximately modeled in the turbulence model.

Praharaj, S. C.↗

NASA NTRS2004

Determination of the Three-Dimensional Morphology of ALH84001 and Biogenic MV-1 Magnetite: Comparison of Results from Electron Tomography and Classical Transmission Electron Microscopy

Dated at approximately 3.9 billion years of age, carbonate disks, found within fractures of the host rock of Martian meteorite ALH84001, have been interpreted as secondary minerals that formed at low temperature in an aqueous medium. Heterogeneously distributed within these disks are magnetite nanocrystals that are of Martian origin. Approximately one quarter of these magnetites have morphological and chemical similarities to magnetite particles produced by magnetotactic bacteria strain MV-1, which are ubiquitous in aquatic habitats on Earth. Moreover, these types of magnetite particles are not known or expected to be produced by abiotic means either through geological processes or synthetically in the laboratory. The remaining three quarters of the ALH84001 magnetites are likely products of multiple processes including, but not limited to, precipitation from a hydrothermal fluid, thermal decomposition of the carbonate matrix in which they are embedded, and extracellular formation by dissimilatory Fe-reducing bacteria. We have proposed that the origins of magnetites in ALH84001 can be best explained as the products of multiple processes, one of which is biological. Recently the three-dimensional (3-D) external morphology of the purported biogenic fraction of the ALH84001 magnetites has been the subject of considerable debate. We report here the 3-D geometry of biogenic magnetite crystals extracted from MV-1 and of those extracted from ALH84001 carbonate disks using a combination of high resolution classical and tomographic transmission electron microscopy (TEM). We focus on answering the following questions: (1) which technique provides adequate information to deduce the 3-D external crystal morphology?; and, (2) what is the precise 3-D geometry of the ALH84001 and MV-1 magnetites?

Thomas-Keprta, Kathie L.↗

NASA NTRS1973

Evaluation of control laws and actuator locations for control systems applicable to deformable astronomical telescope mirrors

Some of the major difficulties associated with large orbiting astronomical telescopes are the cost of manufacturing the primary mirror to precise tolerances and the maintaining of diffraction-limited tolerances while in orbit. One successfully demonstrated approach for minimizing these problem areas is the technique of actively deforming the primary mirror by applying discrete forces to the rear of the mirror. A modal control technique, as applied to active optics, has previously been developed and analyzed. The modal control technique represents the plant to be controlled in terms of its eigenvalues and eigenfunctions which are estimated via numerical approximation techniques. The report includes an extension of previous work using the modal control technique and also describes an optimal feedback controller. The equations for both control laws are developed in state-space differential form and include such considerations as stability, controllability, and observability. These equations are general and allow the incorporation of various mode-analyzer designs; two design approaches are presented. The report also includes a technique for placing actuator and sensor locations at points on the mirror based upon the flexibility matrix of the uncontrolled or unobserved modes of the structure. The locations selected by this technique are used in the computer runs which are described. The results are based upon three different initial error distributions, two mode-analyzer designs, and both the modal and optimal control laws.

Ostroff, A. J.↗

NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗

NASA NTRS2000

Development and Testing of Cooled CMCs for High Thermal Flux Applications

Ceramic Matrix Composites (CMCS) offer the potential for significant weight savings and improved performance for a range of propulsion components utilizing refractory materials. This paper describes the fabrication and testing of functionally graded CMCs produced via a low cost process that represents an order of magnitude cost savings over conventionally fabricated CMCS. Test cylinders were fabricated, characterized and evaluated during exposure to high thermal fluxes of up to 10MW/meters squared at the Laser Hardened Materials Evaluation Laboratory (LHMEL). The bulk density of the CMC tubes was approximately 2.2 grams per cubic centimeters. The performance of cryogenically cooled CMCs was compared with uncooled CMCs against similar thermal loads, and fundamental property data collected for this relatively new breed of CMC. Finally, test thrust cells were fabricated from the functionally graded composite and tested using liquid H2 and O2 propellants at NASA Glen.

Patterson , Mark↗

NASA NTRS2005

Baseline Computational Fluid Dynamics Methodology for Longitudinal-Mode Liquid-Propellant Rocket Combustion Instability

A computational method for the analysis of longitudinal-mode liquid rocket combustion instability has been developed based on the unsteady, quasi-one-dimensional Euler equations where the combustion process source terms were introduced through the incorporation of a two-zone, linearized representation: (1) A two-parameter collapsed combustion zone at the injector face, and (2) a two-parameter distributed combustion zone based on a Lagrangian treatment of the propellant spray. The unsteady Euler equations in inhomogeneous form retain full hyperbolicity and are integrated implicitly in time using second-order, high-resolution, characteristic-based, flux-differencing spatial discretization with Roe-averaging of the Jacobian matrix. This method was initially validated against an analytical solution for nonreacting, isentropic duct acoustics with specified admittances at the inflow and outflow boundaries. For small amplitude perturbations, numerical predictions for the amplification coefficient and oscillation period were found to compare favorably with predictions from linearized small-disturbance theory as long as the grid exceeded a critical density (100 nodes/wavelength). The numerical methodology was then exercised on a generic combustor configuration using both collapsed and distributed combustion zone models with a short nozzle admittance approximation for the outflow boundary. In these cases, the response parameters were varied to determine stability limits defining resonant coupling onset.

Litchford, R. J.↗