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At least 451 records · Page 25

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NASA NTRS1975

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Warming, R. F.↗

NASA NTRS1975

A finite-difference analysis of the nozzle starting process in an expansion tunnel

A suitable finite-difference method for computing the quasi-one-dimensional unsteady flow in an expansion tunnel nozzle was identified. The difference equations are presented along with the appropriate stability limits. A parametric study of the starting process in an expansion tunnel nozzle is made, and acceptable operating conditions were determined.

Weilmuenster, K. J.↗

NASA NTRS1975

Individual differences in human annoyance response to noise

Individual variations in annoyance and in susceptibility to noise were studied to establish a finer definition of the ingredients of the human annoyance response. The study involved interactions among a heterogeneous sample of human subjects, various noise stimuli, and different physical environments of exposure. Significant differences in annoyance ratings among the six noise stimuli, all equated for peak sound pressure level, were found.

Pearson, R. G.↗

NASA NTRS1976

Difference thresholds for judgments of sink rate during the flare

Past studies have shown that touchdown rates of descent (sink rates) are higher in aircraft simulators than in aircraft under similar conditions. The objective of this paper was to use a psychophysical technique to investigate a pilot's ability to distinguish between two different sink rates close to the ground. The pilots observed a collimated computer graphics display of a typical runway with edge, zone, and centerline lights. The results showed that with a forward velocity of 120 knots, pilots could reliably distinguish between a sink rate of 0.5 m/sec (1.7 ft/sec) and 0.9 m/sec (2.9 ft/sec). The results also showed that the absolute rate of sink did not significantly affect the perception of sink rate. Time of sink and total height drop during the sink did affect the minimum detectable difference between sink rates (the differential threshold). The effects were such that a greater time of sink and greater height drop produced lower thresholds

Palmer, E.↗

NASA NTRS1976

Implicit finite-difference procedures for the computation of vortex wakes

Implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows. The partial differential equations in strong conservation-law form are transformed to cluster grid points in regions with large changes in vorticity. In addition to clustering, fourth-order accurate, spatial difference operators are used to help resolve the flow-field gradients. The use of implicit time-differencing permits large time steps to be taken since temporal variations are typically small. Computational efficiency is achieved by approximate factorization. Both two-dimensional and preliminary three-dimensional calculations are described and qualitatively compared with existing experimental data.

Steger, J. L.↗

NASA NTRS1976

A two-dimensional finite difference solution for the transient thermal behavior of tubular solar collector

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.↗

NASA NTRS1976

Application of a novel finite difference method to dynamic crack problems

A versatile finite difference method (HEMP and HEMP 3D computer programs) was developed originally for solving dynamic problems in continuum mechanics. It was extended to analyze the stress field around cracks in a solid with finite geometry subjected to dynamic loads and to simulate numerically the dynamic fracture phenomena with success. This method is an explicit finite difference method applied to the Lagrangian formulation of the equations of continuum mechanics in two and three space dimensions and time. The calculational grid moves with the material and in this way it gives a more detailed description of the physics of the problem than the Eulerian formulation.

Chen, Y. M.↗

NASA NTRS1976

Two-stage chain sampling inspection plans with different sample sizes in the two stages

A further generalization of the family of 'two-stage' chain sampling inspection plans is developed - viz, the use of different sample sizes in the two stages. Evaluation of the operating characteristics is accomplished by the Markov chain approach of the earlier work, modified to account for the different sample sizes. Markov chains for a number of plans are illustrated and several algebraic solutions are developed. Since these plans involve a variable amount of sampling, an evaluation of the average sampling number (ASN) is developed. A number of OC curves and ASN curves are presented. Some comparisons with plans having only one sample size are presented and indicate that improved discrimination is achieved by the two-sample-size plans.

Stephens, K. S.↗

NASA NTRS1977

Auroral energy deposition and neutral composition changes observed simultaneously by ESRO 4 and AE-C at different altitudes

Neutral composition data obtained simultaneously from ESRO 4 and AE-C during geomagnetically disturbed conditions at different altitudes (160 and 230 km) are used to investigate the atmospheric response to geomagnetic storms and to infer information regarding the excitation mechanism. The data are compared with a theoretical model that estimates the composition effects in terms of wind induced diffusion. A parametric study was conducted bearing on the influence of energy deposition at different altitudes and with varying latitudinal extent. In one of the observed events the composition effects at 160 km are substantially smaller than at 230 km for which we inferred by comparison with the theory that the energy mainly was deposited at 150 km altitude over a wide latitude range. Another event required energy deposition at somewhat lower altitudes near 120 km with a more localized energy source. Significant variations of the turbopause level were not necessary to explain the observed variations.

Trinks, H.↗

NASA NTRS1977

Implicit finite difference simulation of flow about arbitrary geometries with application to airfoils

Finite difference procedures are used to solve either the Euler equations or the 'thin layer' Navier-Stokes equations subject to arbitrary boundary conditions. An automatic grid generation program is employed, and because an implicit finite difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. Computed results for both inviscid and viscous flow about airfoils are described and compared to various known solutions.

Steger, J. L.↗

NASA NTRS1977

Measurement of magnetic field aligned potential differences using high resolution conjugate photoelectron energy spectra

Simultaneous high-resolution observations of a distinctive feature in the energy spectrum of conjugate photoelectrons and spacecraft potential relative to the local ionosphere have allowed the net potential difference between magnetic conjugate points at latitudes below the region of low-energy (i.e., lower than 100 eV) auroral electron precipitation to be determined. Measurements made at 300 km from Atmosphere Explorer C show that there is normally no net potential difference between hemispheres in this region, which extended up to invariant latitudes as high as 74 deg. Two types of apparently related anomalous behavior were infrequently observed at high latitudes. During these periods the incident flux of conjugate photoelectrons was either decelerated by about 3 eV or was not detected.

Peterson, W. K.↗

NASA NTRS1977

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Butler, T. D.↗

NASA NTRS1978

The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.

Weatherill, W. H.↗

NASA NTRS1977

Different approaches of spectral analysis

Several approaches to the problem of the calculation of spectral power density of a random function from an estimate of the autocorrelation function were studied. A comparative study was presented of these different methods. The principles on which they are based and the hypothesis implied were pointed out. Some indications on the optimization of the length of the estimated correlation function was given. An example of application of the different methods discussed in this paper was included.

Lacoume, J. L.↗

NASA NTRS1978

Computing LORAN time differences with an HP-25 hand calculator

A program for an HP-25 or HP-25C hand calculator that will calculate accurate LORAN-C time differences is described and presented. The program is most useful when checking the accuracy of a LORAN-C receiver at a known latitude and longitude without the aid of an expensive computer. It can thus be used to compute time differences for known landmarks or waypoints to predict in advance the approximate readings during a navigation mission.

Jones, E. D.↗

NASA NTRS1977

Observed differences in learning ability of heart rate self-regulation as a function of hypnotic susceptibility

Three groups of eight male and female subjects (aged 20-27 yr) categorized by low and high hypnotic susceptibility were taught to control their heart rates by means of an appropriate autogenic therapy/biofeedback technique. The experimental groups were trained by autogenic therapy and biofeedback, while the control group received only biofeedback. Significant differences are observed in all psychological test scores between subjects of high and low hypnotic susceptibility. The results confirm that (1) there are qualitative and quantitative differences between the performance of individuals with high and low hypnotic susceptibility; (2) interindividual-variability tests yield data relevant to individual performance in visceral learning tasks; (3) the combined autogenic therapy/biofeedback/verbal feedback technique is suitable for conditioning large stable autonomic responses in humans; and (4) this kind of conditioning is effective in eliminating or alleviating physiological reactions to some environmental stressors.

Cowings, P. S.↗

NASA NTRS1978

Differences in radar return from ice-covered North Slope Lakes

Comparisons are made between L and X band synthetic aperture radar images of frozen lakes on the North Slope of Alaska and ground truth observations of the nature of their ice covers. It is shown that the differences in radar backscatter observed on different areas of a lake can be correlated with whether or not the lake is frozen completely to the bottom at the site in question. This explanation is reasonable inasmuch as the reflection coefficient associated with the high-dielectric contrast ice/water interface is significantly higher than that associated with a low-contrast ice/soil interface. However, the presence of the ice/water interface cannot be the only condition required for the higher backscatter because the ice/water interface per se would be specular at X and L band frequencies, causing the energy returned from the interface to be reflected away from the radar receiver. The other principal factor contributing to the return of energy from the ice/water interface to the receiver is believed to be the presence in the ice of numerous vertically elongated air bubbles which would act as scatters.

Weeks, W. F.↗

NASA NTRS1978

The Incorporation of Truncated Fourier Series into Finite Difference Approximations of Structural Stability Equations

A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.

Hannah, S. R.↗