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NASA NTRS1986

On star formation in stellar systems. I - Photoionization effects in protoglobular clusters

The progressive ionization and subsequent dynamical evolution of nonhomogeneously distributed low-metal-abundance diffuse gas after star formation in globular clusters are investigated analytically, taking the gravitational acceleration due to the stars into account. The basic equations are derived; the underlying assumptions, input parameters, and solution methods are explained; and numerical results for three standard cases (ionization during star formation, ionization during expansion, and evolution resulting in a stable H II region at its equilibrium Stromgren radius) are presented in graphs and characterized in detail. The time scale of residual-gas loss in typical clusters is found to be about the same as the lifetime of a massive star on the main sequence.

Tenorio-Tagle, G.↗

NASA NTRS1988

Deconvolution results for wide field-of-view radiometer measurements of reflected solar radiation

The measurement of reflected solar radiation by spacecraft wide-field-of-view radiometers is considered analytically, and the method proposed by Smith (1987) for the solution of the discretized governing equations is described and demonstrated. The theoretical basis of the singular-value decomposition method (partitioning the albedo field into observable and unobservable components) is outlined; its application to Nimbus 7 ERB data is explained in detail; and numerical results are presented in graphs and maps and briefly characterized.

Smith, G. Louis↗

NASA NTRS2011

Link Analysis in the Mission Planning Lab

The legacy communications link analysis software currently used at Wallops Flight Facility involves processes that are different for command destruct, radar, and telemetry. There is a clear advantage to developing an easy-to-use tool that combines all the processes in one application. Link Analysis in the Mission Planning Lab (MPL) uses custom software and algorithms integrated with Analytical Graphics Inc. Satellite Toolkit (AGI STK). The MPL link analysis tool uses pre/post-mission data to conduct a dynamic link analysis between ground assets and the launch vehicle. Just as the legacy methods do, the MPL link analysis tool calculates signal strength and signal- to-noise according to the accepted processes for command destruct, radar, and telemetry assets. Graphs and other custom data are generated rapidly in formats for reports and presentations. STK is used for analysis as well as to depict plume angles and antenna gain patterns in 3D. The MPL has developed two interfaces with the STK software (see figure). The first interface is an HTML utility, which was developed in Visual Basic to enhance analysis for plume modeling and to offer a more user friendly, flexible tool. A graphical user interface (GUI) written in MATLAB (see figure upper right-hand corner) is also used to quickly depict link budget information for multiple ground assets. This new method yields a dramatic decrease in the time it takes to provide launch managers with the required link budgets to make critical pre-mission decisions. The software code used for these two custom utilities is a product of NASA's MPL.

McCarthy, Jessica A.↗

NASA NTRS1987

Approximate penetration factors for nuclear reactions of astrophysical interest

The ranges of validity of approximations of P(l), the penetration factor which appears in the parameterization of nuclear-reaction cross sections at low energies and is employed in the extrapolation of laboratory data to even lower energies of astrophysical interest, are investigated analytically. Consideration is given to the WKB approximation, P(l) at the energy of the total barrier, approximations derived from the asymptotic expansion of G(l) for large eta, approximations for small values of the parameter x, applications of P(l) to nuclear reactions, and the dependence of P(l) on channel radius. Numerical results are presented in tables and graphs, and parameter ranges where the danger of serious errors is high are identified.

Humblet, J.↗

NASA NTRS1990

Formulation and evaluation of an analytical model for composite box-beams

A direct method for determining the effective elastic stiffnesses and deformation behavior of composite box-beam (BB) structures is developed analytically, validated, and demonstrated. The BB walls are modeled as orthotropic-ply laminated plates, so that the elastic properties vary both through the thickness and around the BB contour; deformation is described in terms of extension, bending, twisting, shearing, and torsion-related out-of-plane warping. Numerical results for several BB configurations are presented in tables and graphs and compared with experimental data and FEM computations (Stemple and Lee, 1989): good general agreement is obtained for cross-ply, antisymmetric, and symmetric layups, except for symmetric layups with ply orientation angles theta greater than 30 deg. Both out-of-plane warping and transverse shear coupling are found to have significant effects on BB elastic response.

Smith, Edward C.↗

NASA NTRS1986

On the free vibrations of spinning paraboloids

The dynamic behavior of a spinning linear-elastic paraboloid subject to nonaxisymmetric deformation is investigated analytically, applying the Rayleigh-Ritz procedure described by Utku et al. (1983). Energy-density, strain-displacement, and velocity-displacement expressions are generated; expressions for the generalized strain and position vector are derived; and the discretized dynamic equations are obtained. Numerical results obtained with a computer-program implementation of the method are presented in extensive tables and graphs. The effects of spin rate and bending rigidity and results for the special case of a spinning disk are included.

Shoemaker, W. L.↗

NASA NTRS1987

Prospects for Eulerian CFD analysis of helicopter vortex flows

The applicability of current finite-volume CFD algorithms based on the Euler equations to the vortex flow over a helicopter in forward flight is investigated analytically. The general characteristics of the flow are reviewed; existing Euler, Navier-Stokes, perturbation, high-order, and adaptive methods are briefly characterized; and a novel Eulerian/Lagrangian approach with entropy and vorticity corrections is presented in detail. Numerical results for simple convection of a finite-core Lamb vortex moving downstream with its axis perpendicular to the flow are presented in graphs, and the possibility of extending the method to three-dimensional, viscous, and shock flows is discussed.

Drela, Mark↗

NASA NTRS1992

Collision integrals for the interaction of the ions of nitrogen and oxygen in a plasma at high temperatures and pressures

The corrections to the transport cross-sections and collision integrals for Coulomb interactions arising from the application of realistic interaction energies of the ions of nitrogen and oxygen are investigated. Accurate potential-energy curves from an ab initio electronic-structure calculation and a semiclassical description of the scattering are used to determine the difference between the cross-sections for the real interaction forces and a Coulomb force for large values of the Debye shielding parameter. Graphs of the correction to the diffusion and viscosity-collision integrals are presented for temperatures from about 10,000 K to 150,000 K. This correction can be combined with tabulations of the collision integrals for shielded Coulomb potentials to determine the contribution of N(+)-N(+), N(+)-O(+), and O(+)-O(+) interactions to the transport properties of high-temperature air. Analytical forms are fitted to the calculated results to assist this application.

Stallcop, James R.↗

NASA NTRS1986

Initiation of breakdown in slender compressible vortices

The onset of vortex breakdown in compressible flows is investigated analytically for the case in which the flow is axially symmetric, the vortex is isolated, its axis is parallel to the main flow, and the vortex radius is small compared to the breakdown length. The conservation equations for mass, momentum, and energy are formulated and solved numerically using a finite-difference scheme, as described by Krause (1985); numerical results are presented in graphs and briefly characterized.

Krause, E.↗

NASA NTRS1979

A thermal vacuum test optimization procedure

An analytical model was developed that can be used to establish certain parameters of a thermal vacuum environmental test program based on an optimization of program costs. This model is in the form of a computer program that interacts with a user insofar as the input of certain parameters. The program provides the user a list of pertinent information regarding an optimized test program and graphs of some of the parameters. The model is a first attempt in this area and includes numerous simplifications. The model appears useful as a general guide and provides a way for extrapolating past performance to future missions.

Kruger, R.↗

NASA NTRS1988

Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method

The effects of mean-flow incidence, airfoil camber, and airfoil thickness on the incompressible aerodynamics of an oscillating airfoil are investigated theoretically, developing and applying a first-order FEM based on locally analytical solutions (LASs). Laplace equations are used to describe the steady and unsteady harmonic velocity potentials; a body-fitted computational grid is employed; grid-element solutions for both potentials are determined using a numerical LAS method; and the LASs are then assembled to obtain a complete solution. Results for a series of flat-plate and Joukowski airfoils are presented in extensive graphs and discussed in detail.

Chiang, Hsiao-Wei D.↗

NASA NTRS1985

Modal response and noise transmission of composite panels

Noise transmission through flat, angular, fiber-reinforced composite panels is investigated experimentally and analytically. A modal decomposition technique was used to obtain solutions to the governing differential equation of motion. Experimental modal analysis was performed in order to confirm the theoretical results. The test specimens were cross-ply and angle-ply composite panels made of various concentrations of fiberglass, graphite, or aramid fibers embedded in epoxy resion. The experimental results showed good agreement with the theoretical calculations. Graphs of the transmission loss characteristics of the different composite panels are provided.

Grosveld, F. W.↗

NASA NTRS1988

Structural dynamics analysis using an unsymmetric block Lanczos algorithm

A method for reducing the order of a dynamical model of a large structure with arbitrary damping is developed analytically and demonstrated. A Lanczos algorithm is described which can reduce square unsymmetric system matrices to block-tridiagonal form, and a procedure for defining the reduced-order model from the right and left Lanczos vectors is outlined. Results for sample problems involving the 8-DOF FEM model of a beam-rotor assembly subjected to random and stepped external forces are presented in extensive graphs and briefly characterized.

Craig, Roy R., Jr.↗

NASA NTRS1990

Attitude control/momentum management of the Space Station Freedom for large angle torque-equilibrium-attitude configurations

An attitude-control and momentum-management (ACMM) system for the Space Station in a large-angle torque-equilibrium-attitude (TEA) configuration is developed analytically and demonstrated by means of numerical simulations. The equations of motion for a rigid-body Space Station model are outlined; linearized equations for an arbitrary TEA (resulting from misalignment of control and body axes) are derived; the general requirements for an ACMM are summarized; and a pole-placement linear-quadratic regulator solution based on scheduled gains is proposed. Results are presented in graphs for (1) simulations based on configuration MB3 (showing the importance of accounting for the cross-inertia terms in the TEA estimate) and (2) simulations of a stepwise change from configuration MB3 to the 'assembly complete' stage over 130 orbits (indicating that the present ACCM scheme maintains sufficient control over slowly varying Space Station dynamics).

Parlos, Alexander G.↗

NASA NTRS1988

New insights in the numerical reliability properties of existing Kalman filter implementations

The convergence properties of Kalman filter algorithms are investigated analytically. A theoretical error analysis is performed on four types of algorithms, as defined by Anderson and Moore (1979): (1) a conventional Kalman filter, (2) a square-root (SR) covariance filter, (3) the Chandrasekhar SR filter, and (4) an SR information filter. The derivations are given in detail, and numerical results for the flight-path reconstruction problem studied by Verhaegen (1987) are presented in tables and graphs. It is shown that error propagation in algorithms (1) and (2) is sensitive to the condition number of the innovation-signal covariance matrix and the spectral norm of the filter state-transition matrix, whereas other parameters are dominant in (3) and (4). Filter (2) is found to be the most reliable for the class of problems studied.

Verhaegen, M. H.↗

NASA NTRS1987

Fundamental issues in the calculation of rotor wakes

The structure of a helicopter rotor wake and its effects on the aircraft aerodynamics and aeroacoustics are characterized, reviewing the results of recent analytical investigations. The focus is on the role of vortex structure and stability, and consideration is given to Lagrangian computational approaches, two-dimensional and three-dimensional representations of rotor wakes, vortex-sheet rollup computations, and the role of flow instability in the calculation of three-dimensional vortex sheets. Sample results from the author's studies (Sugioka and Widnall, 1985; Kantelis and Widnall, 1986) are presented in graphs and briefly discussed.

Widnall, Sheila↗

NASA NTRS1989

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

The theoretical basis of flexible-aircraft modeling techniques encompassing aerodynamic, control, and elastic-structure effects is investigated analytically, with a focus on methods which employ minimum-state approximations for the unsteady aerodynamics. Rational-function approximations to generalized aerodynamic forces are reviewed; constraints and lag-coefficient optimization are explained; the problem of physical weighting in the minimum-state equations of motion is examined; and results of typical analyses from the NASA Active Flexible Wing project (Perry et al., 1988) are presented in extensive tables and graphs and discussed in detail. The minimum-state approach is shown to produce accurate models at significantly reduced computation costs.

Tiffany, Sherwood H.↗

NASA NTRS1987

The role of damage-softened material behavior in the fracture of composites and adhesives

The failure mechanism of polymer composites and adhesives with high strain in the zone near and ahead of the crack tip is investigated analytically, summarizing the findings of Ungsuwarungsri (1986). A double-cantilever-beam specimen with the nonlinear material confined to a thin strip between two wedge-loaded elastic beams is modeled as a beam on a nonlinear foundation; the two-point boundary-value problem for stationary and propagating cracks is solved numerically; and an FEM approach is applied to study the behavior of the nonlinear strip in detail. Typical results are presented in extensive graphs, and the accuracy and efficiency of the present method are shown to be superior to those of the Berry (1963) procedure.

Ungsuwarungsri, T.↗