Search NASA⌕ Search

SEARCH · Search NASA

Results for “Integral solution”

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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Modeling growth of fatigue cracks which originate at rivet holes

When a structural component is subjected to repeated stress cycles, it can fail at stresses which are well below the tensile strength of the material. The processes leading to this failure are termed fatigue. Instances of fatigue failure in aircraft have become an increasing concern. The crack leading to failure often originate at rivet holes and then grow in response to stress cycles which occur during the operation of the aircraft. A necessary step to preventing failures in todays fleet of aging aircraft is to increase the frequency and quality of inspections; steps were already taken in this direction. There is also a need for modeling of fatigue crack growth in the aircraft structures so that improvements in design can be established and predictions of the life of the components can be made. The purpose is to provide a method to accurately predict the growth of fatigue cracks and to use this method to make predictions about the life of aircraft structural components. The method relies on the formulation and numerical solution of a singular integral equation(s) for an arbitrarily shaped crack(s) which propagate in response to the applied loading. Of special interest to the aging aircraft studies are cracks which originate at circular holes (i.e., rivet holes), but other crack geometries can be treated equally as well.

Mear, Mark E.↗
NASA NTRS1991

Biological production models as elements of coupled, atmosphere-ocean models for climate research

Process models of phytoplankton production are discussed with respect to their suitability for incorporation into global-scale numerical ocean circulation models. Exact solutions are given for integrals over the mixed layer and the day of analytic, wavelength-independent models of primary production. Within this class of model, the bias incurred by using a triangular approximation (rather than a sinusoidal one) to the variation of surface irradiance through the day is computed. Efficient computation algorithms are given for the nonspectral models. More exact calculations require a spectrally sensitive treatment. Such models exist but must be integrated numerically over depth and time. For these integrations, resolution in wavelength, depth, and time are considered and recommendations made for efficient computation. The extrapolation of the one-(spatial)-dimension treatment to large horizontal scale is discussed.

Platt, Trevor↗
NASA NTRS1991

Internal ballistics model update for ASRM dome

A previous report (no. 5-32279, contract NAS8-36955, DO 51) describes the measures taken to adapt the NASA Complex Burning Region Model and code so that is was applicable to the Advanced Solid Rocket Motor as envisioned at that time. The code so modified was called the CBRM-A. CBRM-A could calculate the port volume and burning area for the star, transition, and cylindrically perforated regions of the motor. Described here is a subsequent effort to add computation of port volume and burning area for the Advanced Solid Rocket Motor head dome. Sample output, input, and overview of the models are included. The software was configured in two forms - a stand alone head dome code and a code integrating the head dome solution with the CBRM-A.

Bowden, Mark H.↗
NASA NTRS1991

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.↗
NASA NTRS1992

The long-term behavior of near-circular orbits in a zonal gravity field

A simple solution has been developed for the long term behavior of a near-circular orbit in a zonal gravity field. The solution is obtained by linearizing the singly averaged variational equations of motion and eliminating a degree of freedom with an integral of motion. The resulting solution is expressed in semiequinoctial elements (h and k), and has either an exponential or periodic form. The type of solution is dependent upon a stability factor determined by the inclination and the values of the gravity field coefficients. Frozen orbits correspond to the equilibrium solutions of the set of simplified variational equations. An approximate expression for the location of these orbits has been developed and can be useful for certain mission design applications.

Cook, Richard A.↗
NASA NTRS1992

Computation of unsteady flows over airfoils

Two methods are described for calculating unsteady flows over rapidly pitching airfoils. The first method is based on an interactive scheme in which the inviscid flow is obtained by a panel method. The boundary layer flow is computed by an interactive method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier-Stokes equations. The solution of these equations is obtained with an approximately factorized numerical algorithm, and with single block or multiple grids which enable grid embedding to enhance the resolution at isolated flow regions. In addition, the attached flow region can be computed by the numerical solution of compressible boundary layer equations. Unsteady pressure distributions obtained with both methods are compared with available experimental data.

Ekaterinaris, J. A.↗
NASA NTRS1995

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗
NASA NTRS1995

Optically thick winds: How is the mass flux determined?

Expanding envelopes of compact objects that possess a buring region at the base of the envelope are commonly observed and modeled. In many cases, such as the late stages of classical nova, the expanding envelope develops into a stationary, optically thick wind of matter escaping from the star. In the usual theoretical formalism there is one more unknown than equations, with closure being obtained by the requirement that the solution pass through the singularity at the sonic point. It is shown analytically that the mass flux, which is one of the unknowns, is almost completely determined by the physical conditions near the base of the envelope just above the burning zone. The sonic point closure relation determines whether the expanding solution can develop into a wind solution. For a given core mass the range of possible wind solutions is an outcome of the great sensitivity of the mass flux to the inner luminosity. Solutions determined through numerical integrations are shown to lie entirely within the narrow analytic boundaries.

Glasner, S. Ami↗
NASA NTRS1983

Divergence analysis report for the bodies of revolution model support systems

This report documents the sting divergence analyses of nine different model and model support systems that were performed in preparation for a series of wind tunnel tests at the National Transonic Facility at NASA Langley Research Center in Hampton, Virginia. The models were missile shaped bodies of revolution and the model support systems included a force and moment balance and tapered sting sections. The sting divergence results were obtained from a computer program that solved a two-point boundary value problem which used a second order Runge-Kutta integration technique. The computer solution was based on constant section properties between discrete stations along the sting sections, a procedure was developed and included to evaluate the properties for the minimum number of stations along the tapered sections that would produce no more than one half of one percent error in the divergence results. Also included in the report are development of the aerodynamic input data, listings of all input and output computer data, and summary sheets that highlight the input and the critical sting divergence dynamic pressure for each respective configuration.

Rash, Larry C.↗
NASA NTRS2002

Tightly Coupled Inertial Navigation System/Global Positioning System (TCMIG)

Many NASA applications planned for execution later this decade are seeking high performance, miniaturized, low power Inertial Management Units (IMU). Much research has gone into Micro-Electro-Mechanical System (MEMS) over the past decade as a solution to these needs. While MEMS devices have proven to provide high accuracy acceleration measurements, they have not yet proven to have the accuracy required by many NASA missions in rotational measurements. Therefore, a new solution has been formulated integrating the best of all IMU technologies to address these mid-term needs in the form of a Tightly Coupled Micro Inertial Navigation System (INS)/Global Positioning System (GPS) (TCMIG). The TCMIG consists of an INS and a GPS tightly coupled by a Kalman filter executing on an embedded Field Programmable Gate Array (FPGA) processor. The INS consists of a highly integrated Interferometric Fiber Optic Gyroscope (IFOG) and a MEMS accelerometer. The IFOG utilizes a tightly wound fiber coil to reduce volume and the high level of integration and advanced optical components to reduce power. The MEMS accelerometer utilizes a newly developed deep etch process to increase the proof mass and yield a highly accurate accelerometer. The GPS receiver consists of a low power miniaturized version of the Blackjack receiver. Such an IMU configuration is ideal to meet the mid-term needs of the NASA Science Enterprises and the new launch vehicles being developed for the Space Launch Initiative (SLI).

Watson, Michael D.↗
NASA NTRS1993

The Design of a Primary Flight Trainer using Concurrent Engineering Concepts

Concurrent Engineering (CE) concepts seek to coordinate the expertise of various disciplines from initial design configuration selection through product disposal so that cost efficient design solutions may be achieve. Integrating this methodology into an undergraduate design course sequence may provide a needed enhancement to engineering education. The Advanced Design Program (ADP) project at Embry-Riddle Aeronautical University (EMU) is focused on developing recommendations for the general aviation Primary Flight Trainer (PFT) of the twenty first century using methods of CE. This project, over the next two years, will continue synthesizing the collective knowledge of teams composed of engineering students along with students from other degree programs, their faculty, and key industry representatives. During the past year (Phase I). conventional trainer configurations that comply with current regulations and existing technologies have been evaluated. Phase I efforts have resulted in two baseline concepts, a high-wing, conventional design named Triton and a low-wing, mid-engine configuration called Viper. In the second and third years (Phases II and III). applications of advanced propulsion, advanced materials, and unconventional airplane configurations along with military and commercial technologies which are anticipated to be within the economic range of general aviation by the year 2000, will be considered.

Ladesic, James G.↗
NASA NTRS1999

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

Dunn, M. H.↗
NASA NTRS1949

A Class of De Laval Nozzles

A study is made herein of the irrotational adiabatic motion of a gas in the transition from subsonic to supersonic velocities. A shape of the de Laval nozzle is given, which transforms a homogeneous plane-parallel flow at large subsonic velocity into a supersonic flow without any shockwaves beyond the transition line from the subsonic to the supersonic regions of flow. The method of solution is based on integration near the transition line of the gas equations of motion in the form investigated by S. A. Christianovich.

Falkovich, S. V.↗
NASA NTRS2005

Development of a Thin-Film Solar Cell Interconnect for the Powersphere Concept

Dual junction amorphous silicon (a-Si) solar cells produced on polyimide substrate have been selected as the best candidate to produce a lightweight solar array for the PowerSphere program. The PowerSphere concept features a space-inflatable, geodetic solar array approximately 0.6 meters in diameter and capable of generating about 20W of electrical power. Trade studies of various wiring concepts and connection methods led to an interconnect design with a copper contact that wraps around the edge, to the back of the solar cell. Applying Plasma Vapor Deposited (PVD) copper film to both sides and the edge of the solar cell produces the wrap around contact. This procedure results in a contact pad on the back of the solar cell, which is then laser welded to a flex circuit material. The flex circuit is constructed of copper in a custom designed routing pattern, and then sandwiched in a Kapton insulation layer. The flex circuit then serves as the primary power distribution system between the solar cells and the spacecraft. Flex circuit material is the best candidate for the wiring harness because it allows for low force deployment of the solar cells by the inflatable hinges on the PowerSphere. An additional frame structure, fabricated and assembled by ILC Dover, will reinforce the wrap around contact-flex blanket connection, thus providing a mechanically robust solar cell interconnect for the PowerSphere multifunctional program. The PowerSphere team will use the wraparound contact design approach as the primary solution for solar cell integration and the flex blanket for power distribution.

Simburger, Edward J.↗
NASA NTRS2007

Detergent-Specific Membrane Protein Crystallization Screens

A suite of reagents has been developed for three-dimensional crystallization of integral membranes present in solution as protein-detergent complexes (PDCs). The compositions of these reagents have been determined in part by proximity to the phase boundaries (lower consolute boundaries) of the detergents present in the PDCs. The acquisition of some of the requisite phase-boundary data and the preliminary design of several of the detergent- specific screens was supported by a NASA contract. At the time of expiration of the contract, a partial set of preliminary screens had been developed. This work has since been extended under non-NASA sponsorship, leading to near completion of a set of 20 to 30 different and unique detergent- specific 96-condition screens.

Wiener, Michael↗
NASA NTRS2010

Modeling Broadband X-Ray Absorption of Massive Star Winds

We present a method for computing the net transition of X-rays emitted by shock-heated plasma distributed throughout a partially optically thick stellar wind from a massive star. We find the transmission by an exact integration of the formal solution, assuming the emitting plasma and absorbing plasma are mixed at a constant mass ratio above some minimum radius, below which there is assumed to be no emission. This model is more realistic than either the slab absorption associated with a corona at the base of the wind or the exospheric approximation that assumes all observed X-rays are emitted without attenuation from above the radius of optical depth unity. Our model is implemented in XSPEC as a pre-calculated table that can be coupled to a user-defined table of the wavelength dependent wind opacity. We provide a default wind opacity model that is more representative of real wind opacities than the commonly used neutral ISM tabulation. Preliminary modeling of Chandra grating data indicates that the X-ray hardness trend of OB stars with spectral subtype cars largely be understood as a wind absorption effect.

Leutenegger, Maurice A.↗
NASA NTRS2003

Global Aspects of Charged Particle Motion in Axially Symmetric Multipole Magnetic Fields

The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.

Shebalin, John V.↗
NASA NTRS2012

Low Average Sidelobe Slot Array Antennas for Radiometer Applications

In radiometer applications, it is required to design antennas that meet low average sidelobe levels and low average return loss over a specified frequency bandwidth. It is a challenge to meet such specifications over a frequency range when one uses resonant elements such as waveguide feed slots. In addition to their inherent narrow frequency band performance, the problem is exacerbated due to modeling errors and manufacturing tolerances. There was a need to develop a design methodology to solve the problem. An iterative design procedure was developed by starting with an array architecture, lattice spacing, aperture distribution, waveguide dimensions, etc. The array was designed using Elliott s technique with appropriate values of the total slot conductance in each radiating waveguide, and the total resistance in each feed waveguide. Subsequently, the array performance was analyzed by the full wave method of moments solution to the pertinent integral equations. Monte Carlo simulations were also carried out to account for amplitude and phase errors introduced for the aperture distribution due to modeling errors as well as manufacturing tolerances. If the design margins for the average sidelobe level and the average return loss were not adequate, array architecture, lattice spacing, aperture distribution, and waveguide dimensions were varied in subsequent iterations. Once the design margins were found to be adequate, the iteration was stopped and a good design was achieved. A symmetric array architecture was found to meet the design specification with adequate margin. The specifications were near 40 dB for angular regions beyond 30 degrees from broadside. Separable Taylor distribution with nbar=4 and 35 dB sidelobe specification was chosen for each principal plane. A non-separable distribution obtained by the genetic algorithm was found to have similar characteristics. The element spacing was obtained to provide the required beamwidth and close to a null in the E-plane end-fire direction. Because of the alternating slot offsets, grating lobes called butterfly lobes are produced in non-principal planes close to the H-plane. An attempt to reduce the influence of such grating lobes resulted in a symmetric design.

Rengarajan, Sembiam↗