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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Meteorites may follow a chaotic route to earth

A numerical integration was employed to show that the 3/1 Kirkwood gap region between Jupiter and the sun can serve as the source for asteroidal debris that strikes the earth as chondrites. A previous study by Wetherill (1968) considered planetary close encounters, secular resonances, collisional destruction in space and subsequent atmospheric abrasion of the chondrites. The factors would have resulted in chaotic trajectories for asteroids in the asteroid belt, i.e., eccentricities large enough to make the objects earth-crossing. A sampling of trajectories which could reach large eccentricities is integrated in terms of deterministic solutions of Hamiltonian systems of equations which behave erratically and are dependent on the initial conditions. The examinations successfully predicted a trajectory with a peak eccentricity of 0.652, a time interval of 340,000 yr, and a semimajor axis between 2.4-2.53 AU that was earth-crossing.

Wisdom, J.↗
NASA NTRS1985

Rotordynamic coefficients for compressible flow in tapered annular seals

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs' turbulent bulk-flow model. Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients. Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure. The effects of preswirl and seal taper are shown for three different length-to-diameter ratios. Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness.

Nelson, C. C.↗
NASA NTRS1985

Tolerance bounds for log gamma regression models

The present procedure for finding lower confidence bounds for the quantiles of Weibull populations, on the basis of the solution of a quadratic equation, is more accurate than current Monte Carlo tables and extends to any location-scale family. It is shown that this method is accurate for all members of the log gamma(K) family, where K = 1/2 to infinity, and works well for censored data, while also extending to regression data. An even more accurate procedure involving an approximation to the Lawless (1982) conditional procedure, with numerical integrations whose tables are independent of the data, is also presented. These methods are applied to the case of failure strengths of ceramic specimens from each of three billets of Si3N4, which have undergone flexural strength testing.

Jones, R. A.↗
NASA NTRS1985

Ground based concept for time control of aircraft entering the terminal area

This paper summarizes current research for increasing the efficiency of traffic flow at hub airports by application of four dimensional (4D) guidance techniques. A method for generating 4D guidance commands to control the landing time of aircraft that are not equipped with on-board 4D guidance systems is described. In one possible implementation the commands are generated in an auxiliary processor linked to the ATC host computer and displayed on a controller's monitor in the form of profile descent advisories. Accurate time control is achieved by generating air traffic controller advisories in a ground-based algorithm that combines aerodynamic, thrust and atmospheric models with an efficient numerical integration method. The time accuracy and fuel efficiency achieved when the pilot responds to these advisories were evaluated in a piloted simulation of a transport aircraft.

Erzberger, H.↗
NASA NTRS1986

Advanced Rotordynamic Nonlinear Transient Simulation

Advanced rotordynamic nonlinear transient-simulation program, TRANSIM, developed to predict response of high-performance rotating machinery to variety of forcing functions. Works by modal superposition of rotor and casing subsystems. Transient response of system calculated by numerical integration of equations of motion, performed in modal coordinates. Resulting data transformed back into physical coordinates as required to determine user-requested loads and accelerations as function of time. Used to analyze Space Shuttle main engine high-pressure fuel turbopump. TRANSIM written in FORTRAN 77.

Becht, D. G.↗
NASA NTRS1985

Extension of Ostwald Ripening Theory

The objective is to develop models based on the mean field approximation of Ostwald ripening to describe the growth of second phase droplets or crystallites. The models will include time variations in nucleation rate, control of saturation through addition of solute, precipitating agents, changes in temperature, and various surface kinetic effects. Numerical integration schemes have been developed and tested against the asymptotic solution of Liftshitz, Slyozov and Wagner (LSW). A second attractor (in addition to the LSW distribution) has been found and, contrary to the LSW theory, the final distribution is dependent on the initial distribution. A series of microgravity experiments is being planned to test this and other results from this work.

Baird, J.↗
NASA NTRS1985

Vortex Studies Relating to Boundary Layer Turbulence and Noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Further, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.

Adelman, J. L.↗
NASA NTRS1985

Semiempirical method of determining flow coefficients for pitot rake mass flow rate measurements

Flow coefficients applicable to area-weighted pitot rake mass flow rate measurements are presented for fully developed, turbulent flow in an annulus. A turbulent velocity profile is generated semiempirically for a given annulus hub-to-tip radius ratio and integrated numerically to determine the ideal mass flow rate. The calculated velocities at each probe location are then summed, and the flow rate as indicated by the rake is obtained. The flow coefficient to be used with the particular rake geometry is subsequently obtained by dividing the ideal flow rate by the rake-indicated flow rate. Flow coefficients ranged from 0.903 for one probe placed at a radius dividing two equal areas to 0.984 for a 10-probe area-weighted rake. Flow coefficients were not a strong function of annulus hub-to-tip radius ratio for rakes with three or more probes. The semiempirical method used to generate the turbulent velocity profiles is described in detail.

Trefny, C. J.↗
NASA NTRS1985

Numerical simulation of vortex breakdown

The breakdown of an isolated axisymmetric vortex embedded in an unbounded uniform flow is examined by numerical integration of the complete Navier-Stokes equations for unsteady axisymmetric flow. Results show that if the vortex strength is small, the solution approaches a steady flow and the vortex is stable. If the strength is large enough, the solution remains unsteady and a recirculating zone will appear near the axis, its form and internal structure resembling those of the axisymmetric breakdown bubbles with multi-cells observed by Faler and Leibovich (1978). For apppropriate combinations of flow parameters, the flow reveals quasi-periodicity. Parallel calculations with the quasi-cylindrical approximation indicate that so far as predicting of breakdown is concerned, its results coincide quite well with the results mentioned above. Both show that the vortex breakdown has little concern with the Reynolds number or with the critical classification of the upstream flow, at least for the lower range of Reynolds numbers.

Shi, X.↗
NASA NTRS1986

Simulation and analysis of a geopotential research mission

A computer simulation was performed for a Geopotential Research Mission (GRM) to enable study of the gravitational sensitivity of the range/rate measurement between two satellites and to provide a set of simulated measurements to assist in the evaluation of techniques developed for the determination of the gravity field. The simulation, identified as SGRM 8511, was conducted with two satellites in near circular, frozen orbits at 160 km altitude and separated by 300 km. High precision numerical integration of the polar orbits was used with a gravitational field complete to degree and order 180 coefficients and to degree 300 in orders 0 to 10. The set of simulated data for a mission duration of about 32 days was generated on a Cray X-MP computer. The characteristics of the simulation and the nature of the results are described.

Schutz, B. E.↗
NASA NTRS1985

The range of validity of the two-body approximation in models of terrestrial planet accumulation. II - Gravitational cross sections and runaway accretion

The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact (V/V-sub-e). Impact rates as a function of this ratio are calculated to within about 20 percent by numerical integration of the equations of motion. It is found that when the ratio is greater than 0.4 the two-body approximation is a good one. Consequences of reducing the ratio to less than 0.02 are examined. Factors leading to an optimal size for growth of planetesimals from a swarm of given eccentricity and placing a limit on the extent of runaway accretion are derived.

Wetherill, G. W.↗
NASA NTRS1984

Secular solution for delta-V during spin rate change maneuvers of rigid body spacecraft

Analytic expressions have been found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant body-fixed torques. These solutions have been used to solve for the secular terms in the translational delta-V equations in inertial space. This secular delta-V solution is of interest in application to spinning spacecraft in that it describes the average direction of the delta-V of the spacecraft during a spin-up maneuver. Numerical integration of the governing differential equations has verified that the secular delta-V solution is valid for large time and is accurate in many physical situations including spin-up maneuvers of the Galileo spacecraft.

Klumpe, E. W.↗
NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗
NASA NTRS1986

Analysis of separation of a two-stage winged launch vehicle

The feasibility of separating a two-stage winged, parallel configured launch vehicle at Mach 3 has been determined. The two-stage fully-reusable launch vehicle is comprised of an orbiter, which can be used alone as a single-stage-to-orbit vehicle, and a booster which is identical to the baseline orbiter design. A three-degree-of-freedom analysis was conducted on the ascent trajectory of the two-stage concept to determine the optimum staging conditions. The booster provides all propellant for both stages using a crossfeed system until staging occurs. After staging, the empty booster glides back to the launch site for a horizontal landing. To analyze the separation maneuver, the six-degree-of-freedom equations of motion for both stages were numerically integrated using a computer program which incorporates analytically derived interference aerodynamic data. The necessary conditions for a successful separation were determined and required the use of active controls on both the orbiter and booster. Once the booster and orbiter were separated, a three-degree-of-freedom analysis was conducted on the booster's glideback trajectory.

Naftel, J. C.↗
NASA NTRS1986

Wall reflection of a viscous vortex ring

The behavior of a viscous axisymmetric vortex ring being reflected from a wall is investigated. The incompressible Navier-Stokes equations formulated in terms of the vorticity function and vector potential are numerically integrated by implicit finite difference methods. To specify the vector potential at a far boundary from the wall, the existing integral method used so far only for an unbounded domain is modified by a kind of image method. The trajectory of the vortex ring calcualted as a result closely resembles that observable from the experiment.

Sa, J. Y.↗
NASA NTRS1986

Motion of an electron bunch through a plasma

In space research, pulse-modulated beams, or bunches, of energetic electrons have been used for tracing magnetic field lines and for remote sounding of magnetospheric electric fields. Doubts have been expressed regarding the possibility that an electron bunch would be able to travel through the plasma in space. However, experiments in the ionosphere have shown that, at least on some occasions, bunches of electrons with energies of a few keV have traveled over long distances with no apparent energy loss. The present study is concerned with the theoretical explanation for this phenomenon. The method employed in this study makes use of a direct numerical integration of the Vlasov equation. The results obtained provide the basis for a provisional conclusion concerning the stability of a moving electron bunch in the considered case. It appears that the system is mildly unstable.

Shoucri, M. M.↗
NASA NTRS1985

Navigation systems

The elements of the measurement and communications network comprising the global deep space navigation system (DSN) for NASA missions are described. Among the measurement systems discussed are: VLBI, two-way Doppler and range measurements, and optical measurements carried out on board the spacecraft. Processing of navigation measurement is carried out using two modules: an N-body numerical integration of the trajectory (and state transition partial derivatives) based on pre-guessed initial conditions; and partial derivatives of simulated observables corresponding to each actual observation. Calculations of velocity correction parameters is performed by precise modelling of all physical phenomena influencing the observational measurements, including: planetary motions; tracking station locations, gravity field structure, and transmission media effects. Some of the contributions to earth-relative orbit estimate errors for the Doppler/range system on board Voyager are discussed in detail. A line drawing of the DSN navigation system is provided.

Jordan, J. F.↗
NASA NTRS1986

The cosmic-ray source composition

The cosmic-ray source composition is shown to be related to the observed cosmic-ray abundances by a set of linear equations which are valid for either ad hoc path length distributions or quantitative solutions of galactic propagation models. In the limit of no ionization energy loss, this method is exact for all path length distributions and can replace more detailed numerical integrations; it provides a simple way to calculate directly the source composition implied by a particular set of cross sections, observed abundances, and propagation model. This method is used to determine the source abundances of the galactic cosmic rays in a model-independent manner. Compared to a simple exponential, the path length distribution required by observations is deficient in the contributions from short (not greater than 0.5 g/sq cm) paths at energies of a few GeV per nucleon.

Margolis, S. H.↗