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Results for “Approximation methods”

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.

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At least 1,351 records · Page 75
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

An experimental investigation of surface pressure measurements on an advanced winged entry vehicle at Mach 10

Surface pressure measurements have been made at Mach 10 in air on an instrumented 0.006-scale model of an advanced (control configured) winged entry vehicle. The tests were conducted in the Langley Continuous Flow Hypersonic Tunnel. Data were obtained at 83 surface pressure stations, which include locations on the lower and upper surface centerlines, spanwise positions along the lower and upper surfaces of the wing, the lower surface of the body flap, and radial locations on the fuselage. Data were obtained for angles of attack ranging from zero to 40 deg, sideslip angles of -2 deg to +5 deg, Reynolds numbers of 0.5, 1.0, and 2.0 million per foot, and body-flap deflections of zero, 10, and 20 deg. Test conditions and orifice locations were chosen to correspond directly with those for the heat transfer measurements previously reported on the same configuration. Comparison of windward symmetry plane data with predictions based upon an approximate engineering method was found to yield reasonable agreement for angles of attack from 20 to 40 deg. The leeward surface pressure data were observed to be roughly an order of magnitude lower than the corresponding windward data. At low angles of attack, regions of high pressure were noted on the windward wing surface. The result is attributed to vortical action or shock impingement. High pressures were also measured on the deflected body flap, a critical region for this type of vehicle. Reynolds number effects were found to be insignificant.

Wurster, K. E.↗
NASA NTRS1985

Spatial variation of cosmic rays near the heliospheric current sheet

A quantitative comparison between theoretical predictions and observations of the intensity of galactic cosmic rays near the interplanetary current sheet is reported. Comparison of model calculations is made with a statistical analysis of observations of galactic cosmic rays at Earth and the simultaneous position of the current sheet. An ensemble of different current sheet inclinations is used, in order to make the analysis of the computations approximate the method used to analyses the data.

Jokipii, J. R.↗
NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗
NASA NTRS1985

Nonlinear Dynamics of a Helicopter Model in Ground Resonance

An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis.

Tang, D. M.↗
NASA NTRS1986

Investigation of solid plume simulation criteria to produce flight plume effects on multibody configuration in wind tunnel tests

An investigation to determine the sensitivity of the space shuttle base and forebody aerodynamics to the size and shape of various solid plume simulators was conducted. Families of cones of varying angle and base diameter, at various axial positions behind a Space Shuttle launch vehicle model, were wind tunnel tested. This parametric evaluation yielded base pressure and force coefficient data which indicated that solid plume simulators are an inexpensive, quick method of approximating the effect of engine exhaust plumes on the base and forebody aerodynamics of future, complex multibody launch vehicles.

Frost, A. L.↗
NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗
NASA NTRS1986

Multigrid acceleration of the flux split Euler equations

Multigrid acceleration is applied to a flux-split algorithm for solving the Euler equations in two and three dimensions. The basic algorithm is an implicit spatially-split approximate factorization method. The stability of the scheme in comparison to other factorization is examined. Results are presented for two-dimensional airfoil flows and three-dimensional wing flows which demonstrate substantially improved convergence with the multigrid algorithm. An asymptotic spectral radius of 0.89 and 0.93 is attained for a 97 x 17 x 17 wing solution at subcritical and supercritical conditions, respectively.

Anderson, W. K.↗
NASA NTRS1986

Cosmic rays near the heliospheric current sheet. II - An ensemble approach to comparing theory and observation

A quantitative comparison is carried out between theoretical predictions and observations of the intensity of galactic cosmic rays near the interplanetary current sheet. Model calculations are compared with a statistical analysis of observations of galactic cosmic rays at the earth and the simultaneous position of the current sheet. Since the observations were made over a period of several years, the inclination of the current sheet varied considerably, and comparison with any one model calculation referring to a given inclination would not be appropriate. An ensemble of different current sheet inclinations are used to generate expected values with the model in order to make the analysis of the computations approximate the method used to analyze the data. Agreement is found between theory and observation at energies of the order of a few GeV.

Jokipii, J. R.↗
NASA NTRS1987

Finite element analysis of flexible, rotating blades

A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.

Mcgee, Oliver G.↗
NASA NTRS1986

Data inversion algorithm development for the hologen occultation experiment

The successful retrieval of atmospheric parameters from radiometric measurement requires not only the ability to do ideal radiometric calculations, but also a detailed understanding of instrument characteristics. Therefore a considerable amount of time was spent in instrument characterization in the form of test data analysis and mathematical formulation. Analyses of solar-to-reference interference (electrical cross-talk), detector nonuniformity, instrument balance error, electronic filter time-constants and noise character were conducted. A second area of effort was the development of techniques for the ideal radiometric calculations required for the Halogen Occultation Experiment (HALOE) data reduction. The computer code for these calculations must be extremely complex and fast. A scheme for meeting these requirements was defined and the algorithms needed form implementation are currently under development. A third area of work included consulting on the implementation of the Emissivity Growth Approximation (EGA) method of absorption calculation into a HALOE broadband radiometer channel retrieval algorithm.

Gordley, Larry L.↗
NASA NTRS1986

Topographic effect on tilt, strain, and displacement measurements

An approximate analytical method is used to give simple expressions for the effect of arbitrarily shaped topography on vertical, horizontal and surface tilt measurements. Corrections to tilt fields are found to be directly proportional to the local slope of the topography. Comparison is made between expressions for tilt and those for strain and displacement. Although the topographic effects on secular tilt, strain, and vertical displacement are not yet measurable, the topographic effect on precision tidal tilt and strain measurements can be significant.

Meertens, Charles M.↗
NASA NTRS1988

Accurate collision-induced line-coupling parameters for the fundamental band of CO in He - Close coupling and coupled states scattering calculations

The first accurate theoretical values for off-diagonal (i.e., line-coupling) pressure-broadening cross sections are presented. Calculations were done for CO perturbed by He at thermal collision energies using an accurate ab initio potential energy surface. Converged close coupling, i.e., numerically exact values, were obtained for coupling to the R(0) and R(2) lines. These were used to test the coupled states (CS) and infinite order sudden (IOS) approximate scattering methods. CS was found to be of quantitative accuracy (a few percent) and has been used to obtain coupling values for lines to R(10). IOS values are less accurate, but, owing to their simplicity, may nonetheless prove useful as has been recently demonstrated.

Green, Sheldon↗
NASA NTRS1988

Single-grid spectral collocation for the Navier-Stokes equations

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

Bernardi, Christine↗
NASA NTRS1989

Effect of ephemeris errors on the accuracy of the computation of the tangent point altitude of a solar scanning ray as measured by the SAGE 1 and 2 instruments

An analysis was made of the error in the minimum altitude of a geometric ray from an orbiting spacecraft to the Sun. The sunrise and sunset errors are highly correlated and are opposite in sign. With the ephemeris generated for the SAGE 1 instrument data reduction, these errors can be as large as 200 to 350 meters (1 sigma) after 7 days of orbit propagation. The bulk of this error results from errors in the position of the orbiting spacecraft rather than errors in computing the position of the Sun. These errors, in turn, result from the discontinuities in the ephemeris tapes resulting from the orbital determination process. Data taken from the end of the definitive ephemeris tape are used to generate the predict data for the time interval covered by the next arc of the orbit determination process. The predicted data are then updated by using the tracking data. The growth of these errors is very nearly linear, with a slight nonlinearity caused by the beta angle. An approximate analytic method is given, which predicts the magnitude of the errors and their growth in time with reasonable fidelity.

Buglia, James J.↗
NASA NTRS1989

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Rumsey, Christopher L.↗
NASA NTRS1989

Molecular cloud cores and bimodal star formation

The phenomenon of bimodal star formation is reviewed in the context of supercritical and subcritical states for molecular clouds that are supported against their self-gravitation by magnetic fields. The governing set of equations is derived subject to the quasi-static and axisymmetric approximations. The method of numerical solution and tests of the resultant computer code are outlined. The results of the evolutionary calculations are discussed, emphasizing time scales, masses, and typical sizes of modeled cores that can be compared with observations. For a fixed mass, it is found that the level or turbulent support determines whether a dense core forms or not. This is used to generalize the concept of a critical mass to account for the contributions of turbulence and thermal pressures to the support of a cloud.

Lizano, Susana↗
NASA NTRS1989

On the design of nonlinear controllers for flight control systems

A method of approximate input-output linearization by dynamic state feedback is presented, with the flight control of VTOL aircraft used as an example. It is shown that the closed loop system has a graceful degradation of performance as the moment-to-force coupling is increased. It is also demonstrated that the approach proposed here leads to an asymptotically stable closed loop system with guaranteed bounds on the tracking error caused by the nonminumum phase character of the system.

Hauser, John↗