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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

A mathematical analysis of the theory of interplanetary scintillation in the weak scattering approximation

A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.

Mitchell, D. G.↗
NASA NTRS2001

Numerical Study of g-Jitter Induced Double-Diffusive Convection

A finite element study is presented of double-diffusive convection driven by g-jitter in a microgravity environment. Mathematical formulations are presented and extensive simulations are carried out for g-jitter induced fluid flow, temperature distribution, and solutal transport in an alloy system under consideration for space flights. Computations include the use of idealized single-frequency and multi-frequency g-jitter as well as the real g-jitter data taken during an actual Space Shuttle fight. Little correlation is seen between these velocity components for the g-jitter components studied. The temperature field is basically undisturbed by convection because of a small Pr number for the fluid. The disturbance of the concentration field, however, is pronounced, and the local variation of the concentration follows the velocity oscillation in time. It is found that although the concentration field varies in both position and time, the local concentration gradient remains approximately constant in time. Numerical study further indicates that with an increase in g-jitter force (or amplitude), the nonlinear convective effects become much more obvious, which in turn drastically change the concentration fields. The simulated results computed using the g-jitter data taken during space flights show that both the velocity and concentration become random, following approximately the same pattern as the g-jitter perturbations.

Shu, Y.↗
NASA NTRS1979

On the Routh approximation technique and least squares errors

A new method for calculating the coefficients of the numerator polynomial of the direct Routh approximation method (DRAM) using the least square error criterion is formulated. The necessary conditions have been obtained in terms of algebraic equations. The method is useful for low frequency as well as high frequency reduced-order models.

Aburdene, M. F.↗
NASA NTRS1997

Effect of microgravity and hypergravity on deposition of 0.5- to 3-micron-diameter aerosol in the human lung

We measured intrapulmonary deposition of 0. 5-, 1-, 2-, and 3-micron-diameter particles in four subjects on the ground (1 G) and during parabolic flights both in microgravity (microG) and at approximately 1.6 G. Subjects breathed aerosols at a constant flow rate (0.4 l/s) and tidal volume (0.75 liter). At 1 G and approximately 1.6 G, deposition increased with increasing particle size. In microG, differences in deposition as a function of particle size were almost abolished. Deposition was a nearly linear function of the G level for 2- and 3-micron-diameter particles, whereas for 0.5- and 1.0-micron-diameter particles, deposition increased less between microG and 1 G than between 1 G and approximately 1.6 G. Comparison with numerical predictions showed good agreement for 1-, 2-, and 3-micron-diameter particles at 1 and approximately 1.6 G, whereas the model consistently underestimated deposition in microG. The higher deposition observed in microG compared with model predictions might be explained by a larger deposition by diffusion because of a higher alveolar concentration of aerosol in microG and to the nonreversibility of the flow, causing additional mixing of the aerosols.

Flight Experiment↗
NASA NTRS1976

Dynamics of spin stabilized spacecraft during deployment of telescoping appendages

The dynamics of a spin stabilized spacecraft with telescoping appendages are treated both analytically and numerically. Two types of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution. For the more general case, a series solution is obtained and this solution is limited by its radius of convergence. The comparison of the different approximate analytical methods with numerical integration results are studied and it is observed that the oscillatory nature of the responses of the transverse angular velocity components reduces rapidly with faster extension rates.

Sellappan, R.↗
NASA NTRS1974

Aeroelastic stability of periodic systems with application to rotor blade flutter

The dynamics of a helicopter blade in forward flight are described by a system of linear differential equations with periodic coefficients. The stability of this periodic aeroelastic system is determined, using multivariable Floquet-Liapunov theory. The transition matrix at the end of the period is evaluated by: (1) direct numerical integration, and (2) a new, approximate method, which consists in approximating a periodic function by a series of step functions. The numerical accuracy and efficiency of the methods is compared, and the second method is shown to be superior by far. Results illustrating the effect of the periodic coefficients and various blade parameters are presented.

Friedmann, P.↗
NASA NTRS1984

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

Connor, J. N. L.↗
NASA NTRS2005

Benchmark Problems Used to Assess Computational Aeroacoustics Codes

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

Dahl, Milo D.↗
NASA NTRS1995

On the breakup of viscous liquid threads

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Papageorgiou, Demetrios T.↗
NASA NTRS1994

Measuring the Hubble constant and our Virgo-infall velocity independently

A sample of spiral galaxies with B(sub T) less than 14.5 located in two local volumes, one in the direction of, but behind, the Virgo Cluster (behind-Virgo volume (BV)) and the other in the opposite direction (anti-Virgo volume (AV)), were used via a Tully-Fisher (TF) relation to derive the following two parameters: H(sub AB), the mean Hubble ratio between AV and BV, and delta v(sub parallel), the peculiar velocity of the Local Group in the direction of the Virgo Cluster (VC) with respect to a uniformly expanding reference system defined by our AV and BV sub-samples. The two sampled volumes, separated by a velocity interval of 5600 km/s, form an antipodal pair. This particular geometry not only allows us to derive the two parameters independently but also reduces the dynamical effect of the Local Supercluster on H(sub AB) without increasing the Malmquist bias. By limiting our sample to spiral galaxies having large velocity widths W(sub R), we effectively reduce the TF scatter and Malmquist bias in our sample. The TF zero point and dispersion were then determined by further correcting for the small residual Malmquist bias. An additional sample of fainter galaxies was used to test for a non-Gaussian tail to the TF disperison. We found no evidence for such a tail and formally give an upper limit of about 18% for the fractional contribution of an unseen tail. The average intrinsic TF dispersion for the dominant Gaussian component is sigma(sub TF)(sup 0) approximately 0.33 mag for W(sub R) approximately equal to or greater than 180 km/s. Our numerical results are delta v(sub parallel) approximately equals 414 +/- 82 km/s and H(sub AB) approximately equals (84.0 +/- 2.4)(1 + epsilon) km/s Mpc, where (1 + epsilon) accounts for any systematic error between the calibrators and the sample galaxies. Various dynamical models were tested to explore the effect on H(sub AB) of the uncertainties in the local velocity field. Constrained by our observed delta v(sub parallel) as well as other observational quantities, we found that the rms deviation from unity of H(sub AB)/H(sub 0) (where H(sub 0) is the Hubble constant for each model) is 5%, making H(sub AB) a good indicator for H(sub 0). Taking this variation as an additional error, our formal estimate for the Hubble constant is H(sub 0) approximately equals (84 +/- 5)(1 + epsilon) km/s Mpc.

Lu, Nanyao Y.↗
NASA NTRS1974

Analytic approximations in the study of the solar modulation of electrons

Numerical solutions to the transport equation of galactic cosmic rays in the interplanetary medium have been used to investigate the applicability of commonly used approximate analytic solutions for electrons (10 MeV to 10 GeV). We find that for a given cosmic-ray diffusion coefficient the force-field approximation is in reasonable agreement with the numerical solution at energies above 200 MeV, but deviates significantly at lower energies, depending on the shape of the interstellar electron spectrum. The diffusion-convection approximation agrees generally with the numerical solution within a factor of 2 over the entire energy range.

Cummings, A. C.↗
NASA NTRS1979

Simulation of three-dimensional compressible viscous flow on the Illiac IV computer

Complicated three-dimensional viscous transonic flows about bodies at high angles of attack are solved on the Illiac IV computer. It is shown that certain approximate forms of the compressible Reynolds-averaged Navier-Stokes equations can be computed about realistic three-dimensional geometries with relative ease on the Illiac IV. The ease and efficiency with which this can be done depend on the approximations made in the basic equations, the choice of the numerical algorithm used for the solution, and the data-base system that controls the data management and identifies and manipulates the vectors. A pencil data-base system is found to be particularly suitable for the approximations and numerical method chosen to produce the results presented. In addition, some comparisons are made of computer predictions with experimental results for various lows about hemisphere-cylinders in both subsonic and supersonic free streams. The same viscous model and numerical model are used, showing good qualitative agreement in the location of separation lines and pressure distributions.

Pulliam, T. H.↗
NASA NTRS1991

Physically weighted approximations of unsteady aerodynamic forces using the minimum-state method

The Minimum-State Method for rational approximation of unsteady aerodynamic force coefficient matrices, modified to allow physical weighting of the tabulated aerodynamic data, is presented. The approximation formula and the associated time-domain, state-space, open-loop equations of motion are given, and the numerical procedure for calculating the approximation matrices, with weighted data and with various equality constraints are described. Two data weighting options are presented. The first weighting is for normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms, at the expense of less important ones. The resulting approximate yields a relatively low number of aerodynamic lag states in the subsequent state-space model. The formulation forms the basis of the MIST computer program which is written in FORTRAN for use on the MicroVAX computer and interfaces with NASA's Interaction of Structures, Aerodynamics and Controls (ISAC) computer program. The program structure, capabilities and interfaces are outlined in the appendices, and a numerical example which utilizes Rockwell's Active Flexible Wing (AFW) model is given and discussed.

Karpel, Mordechay↗
NASA NTRS1968

Model for high-energy charge transfer.

High energy charge transfer one dimensional model solved numerically and compared to approximations, noting proton-H collisions and atomic excitation by protons

Mittleman, M. H.↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Lancaster, J. E.↗