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NASA NTRS2007

The Extrapolation of High Altitude Solar Cell I(V) Characteristics to AM0

The high altitude aircraft method has been used at NASA GRC since the early 1960's to calibrate solar cell short circuit current, ISC, to Air Mass Zero (AMO). This method extrapolates ISC to AM0 via the Langley plot method, a logarithmic extrapolation to 0 air mass, and includes corrections for the varying Earth-Sun distance to 1.0 AU and compensating for the non-uniform ozone distribution in the atmosphere. However, other characteristics of the solar cell I(V) curve do not extrapolate in the same way. Another approach is needed to extrapolate VOC and the maximum power point (PMAX) to AM0 illumination. As part of the high altitude aircraft method, VOC and PMAX can be obtained as ISC changes during the flight. These values can then the extrapolated, sometimes interpolated, to the ISC(AM0) value. This approach should be valid as long as the shape of the solar spectra in the stratosphere does not change too much from AMO. As a feasibility check, the results are compared to AMO I(V) curves obtained using the NASA GRC X25 based multi-source simulator. This paper investigates the approach on both multi-junction solar cells and sub-cells.

Snyder, David B.↗

NASA NTRS1975

New methods for the numerical integration of ordinary differential equations and their application to the equations of motion of spacecraft

A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.

Banyukevich, A.↗

NASA NTRS1999

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗

NASA NTRS1974

A reevaluation of the interrupter technique for airway resistance measurement

An attempt was made to obtain a better insight into the actual transient response of airway opening pressure (Pao) following rapid occlusion. With this knowledge it was hoped to be able to clarify the reason for the overestimations found by other investigators, and possibly to obtain a more accurate method of estimating alveolar pressure just prior to interruption. This would result in an improved method for estimating airway resistance. Use of an extrapolation method was found to provide an improved correlation between resistances determined by the interruptor technique and those found by the plethysmograph in normal subjects.

Jackson, A. C.↗

NASA NTRS1992

Solution of the Schroedinger equation for a double minimum potential

We apply Richardson's extrapolation to zero mesh size to calculate the dissociation energies and wavefunctions of a double minimum potential curve for the E,F1Sigma(+)g state of H2. We demonstrate that a double minimum potential presents no difficulties and that this extrapolation method is to be preferred over a quadratic extrapolation or the use of a basis expansion.

Goorvitch, D.↗

NASA NTRS2013

Fracture Mechanics Analyses for Interface Crack Problems - A Review

Recent developments in fracture mechanics analyses of the interfacial crack problem are reviewed. The intent of the review is to renew the awareness of the oscillatory singularity at the crack tip of a bimaterial interface and the problems that occur when calculating mode mixity using numerical methods such as the finite element method in conjunction with the virtual crack closure technique. Established approaches to overcome the nonconvergence issue of the individual mode strain energy release rates are reviewed. In the recent literature many attempts to overcome the nonconvergence issue have been developed. Among the many approaches found only a few methods hold the promise of providing practical solutions. These are the resin interlayer method, the method that chooses the crack tip element size greater than the oscillation zone, the crack tip element method that is based on plate theory and the crack surface displacement extrapolation method. Each of the methods is validated on a very limited set of simple interface crack problems. However, their utility for a wide range of interfacial crack problems is yet to be established.

Krueger, Ronald↗

NASA NTRS1992

Siderophile elements and the earth's formation

Two comments on a work by Murthy (1991) concerning the abundances of siderophile elements in the earth's mantle are presented. In the first comment it is asserted that the basis of Murthy's extrapolation is the assumption that the Gibbs free energy change for the partitioning reaction is independent of temperature, and as this is generally not a valid assumption thermodynamically, and as this is contradicted by most experimental data, the issue of mantle siderophile elements remains unresolved. In the second comment it is asserted that the extrapolation method used by Murthy does not appear to be valid thermodynamically, and that an extrapolation based on generally accepted thermodynamic assumptions yields different results. In a reply, Murthy takes issue with the comments.

Jones, J. H.↗

NASA NTRS1997

Investigation of Alert Zone and Display Concepts for Free Flight

To better understand the potential benefits and drawbacks of utilizing a probability-based method, a number of alternative approaches to the collision avoidance problem were examined and summarized in the paper "Survey of Conflict Detection and Resolution Modeling Methods" which was presented in August 1997 at the AIAA Guidance, Navigation, and Control Conference. The paper provides a summary and comparative evaluation of the many different approaches that have been used in the past to perform conflict analysis. Each method is categorized in its dynamic modeling approach and method of handling conflict detection and conflict resolution. For example, one category included the extrapolation method used to predict future trajectories of which 3 were defined: nominal, probabilistic, and worst-case. Another category listed the metrics and parameters used by each method to make conflict decisions (i.e. estimated time to closest point of approach, miss distance, current separation, expected maneuvering cost, probability of conflict). Other useful information such as the ability to handle multi-aircraft conflicts and cooperative and non-cooperative maneuvering is also included.

Yang, Lee C.↗

NASA NTRS1994

High speed civil transport: Sonic boom softening and aerodynamic optimization

An improvement in sonic boom extrapolation techniques has been the desire of aerospace designers for years. This is because the linear acoustic theory developed in the 60's is incapable of predicting the nonlinear phenomenon of shock wave propagation. On the other hand, CFD techniques are too computationally expensive to employ on sonic boom problems. Therefore, this research focused on the development of a fast and accurate sonic boom extrapolation method that solves the Euler equations for axisymmetric flow. This new technique has brought the sonic boom extrapolation techniques up to the standards of the 90's. Parallel computing is a fast growing subject in the field of computer science because of its promising speed. A new optimizer (IIOWA) for the parallel computing environment has been developed and tested for aerodynamic drag minimization. This is a promising method for CFD optimization making use of the computational resources of workstations, which unlike supercomputers can spend most of their time idle. Finally, the OAW concept is attractive because of its overall theoretical performance. In order to fully understand the concept, a wind-tunnel model was built and is currently being tested at NASA Ames Research Center. The CFD calculations performed under this cooperative agreement helped to identify the problem of the flow separation, and also aided the design by optimizing the wing deflection for roll trim.

Cheung, Samson↗

NASA NTRS1989

Quotient-difference type generalizations of the power method and their analysis

The recursion relations that were proposed by W. F. Ford and A. Sidi (Appl. Numer. Math, 4 (1988), pp. 477-489) for implementing vector extrapolation methods are used for devising generalizations of the power method for linear operators. These generalizations are shown to produce approximations to largest eigenvalues of a linear operator under certain conditions. They are similar in form to the quotient-difference algorithm and share similar convergence properties with the latter. These convergence properties also resemble those obtained for the basic LR and QR algorithms. Finally, it is shown that the convergence rate produced by one fo these generalizations is twice as fast for normal operators as it is for nonnormal operators.

Sidi, Avram↗

NASA NTRS1977

Prognosis of the state of health of a person under spaceflight conditions

Methods of predicting the state of health and human efficiency during space flight are discussed. Diversity of reactions to the same conditions, development of extrapolation methods of prediction, and isolation of informative physiological indexes are among the factors considered.

Source record↗

NASA NTRS1991

CFD prediction of the near-field sonic boom environment for two low boom HSCT configurations

Current efforts to reduce the sonic boom of a future High Speed Civil Transport (HSCT) by careful shaping have led to the need for more accurate predictions of the near-field flow conditions of the configuration. A fully three-dimensional Euler finite volume code is used to predict sonic boom pressure signatures for two low boom concepts - one designed to cruise at Mach 2 and the other at Mach 3. Calculations were carried out using a grid topology that has been modified to reduce the inaccuracies caused by grid spreading often suffered with CFD methods when calculations several body lengths downstream become necessary. Comparisons of CFD results and experimental wind tunnel signatures are shown. Ground signatures are predicted by extrapolating the pressures predicted by the Euler code with an extrapolation method based on the Whitham theory.

Siclari, M. J.↗

NASA NTRS1989

On an efficient and accurate method to integrate restricted three-body orbits

This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.

Murison, Marc A.↗

NASA NTRS2006

A Sub-filter Scale Noise Equation far Hybrid LES Simulations

Hybrid LES/subscale modeling approaches have an important advantage over the current noise prediction methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence . Previous hybrid approaches use approximate statistical techniques or extrapolation methods to obtain the requisite information about the sub-filter scale motion. An alternative approach would be to adopt the modeling techniques used in the current noise prediction methods and determine the unknown stresses from experimental data. The present paper derives an equation for predicting the sub scale sound from information that can be obtained with currently available experimental procedures. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid techniques.

Goldstein, Marvin E.↗

NASA NTRS2019

Equilibrium Climate Sensitivity Estimated by Equilibrating Climate Models

The methods to quantify equilibrium climate sensitivity are still debated. We collect millennial length simulations of coupled climate models and show that the global mean equilibrium warming is higher than those obtained using extrapolation methods from shorter simulations. Specifically, 27 simulations with 15 climate models forced with a range of CO2 concentrations show a median 17% larger equilibrium warming than estimated from the first 150 years of the simulations. The spatial patterns of radiative feedbacks change continuously, in most regions reducing their tendency to stabilizing the climate. In the equatorial Pacific, however, feedbacks become more stabilizing with time. The global feedback evolution is initially dominated by the tropics, with eventual substantial contributions from the midlatitudes. Time dependent feedbacks underscore the need of a measure of climate sensitivity that accounts for the degree of equilibration, so that models, observations, and paleo proxies can be adequately compared and aggregated to estimate future warming.

Maria Rugenstein↗

NASA NTRS1998

Reduction and Analysis of Phosphor Thermography Data With the IHEAT Software Package

Detailed aeroheating information is critical to the successful design of a thermal protection system (TPS) for an aerospace vehicle. This report describes NASA Langley Research Center's (LaRC) two-color relative-intensity phosphor thermography method and the IHEAT software package which is used for the efficient data reduction and analysis of the phosphor image data. Development of theory is provided for a new weighted two-color relative-intensity fluorescence theory for quantitatively determining surface temperatures on hypersonic wind tunnel models; an improved application of the one-dimensional conduction theory for use in determining global heating mappings; and extrapolation of wind tunnel data to flight surface temperatures. The phosphor methodology at LaRC is presented including descriptions of phosphor model fabrication, test facilities and phosphor video acquisition systems. A discussion of the calibration procedures, data reduction and data analysis is given. Estimates of the total uncertainties (with a 95% confidence level) associated with the phosphor technique are shown to be approximately 8 to 10 percent in the Langley's 31-Inch Mach 10 Tunnel and 7 to 10 percent in the 20-Inch Mach 6 Tunnel. A comparison with thin-film measurements using two-inch radius hemispheres shows the phosphor data to be within 7 percent of thin-film measurements and to agree even better with predictions via a LATCH computational fluid dynamics solution (CFD). Good agreement between phosphor data and LAURA CFD computations on the forebody of a vertical takeoff/vertical lander configuration at four angles of attack is also shown. In addition, a comparison is given between Mach 6 phosphor data and laminar and turbulent solutions generated using the LAURA, GASP and LATCH CFD codes. Finally, the extrapolation method developed in this report is applied to the X-34 configuration with good agreement between the phosphor extrapolation and LAURA flight surface temperature predictions. The phosphor process outlined in the paper is believed to provide the aerothermodynamic community with a valuable capability for rapidly obtaining (4 to 5 weeks) detailed heating information needed in TPS design.

Merski, N. Ronald↗

NASA NTRS1973

A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

Thompson, J. F.↗

NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗