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NASA NTRS1992

Secondary instability in three-dimensional magnetic reconnection

We consider the transition to turbulence in three-dimensional reconnection of a magnetic neutral sheet. We find that the transition can occur via a three-step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two-dimensional quasi-steady state. Third, this secondary equilibrium is itself unstable when it is perturbed by three-dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three-dimensional linear stability properties of the two-dimensional saturated tearing layer. The numerical simulations are performed with a semi-implicit, pseudospectral-Fourier collocation algorithm. We identify a three-dimensional secondary linear stability which grows on the ideal timescale. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three-dimensional field, with the two-dimensional field acting as a catalyst.

Dahlburg, R. B.↗

NASA NTRS1993

Acoustic radiation damping of flat rectangular plates subjected to subsonic flows

The acoustic radiation damping for various isotropic and laminated composite plates and semi-infinite strips subjected to a uniform, subsonic and steady flow has been predicted. The predictions are based on the linear vibration of a flat plate. The fluid loading is characterized as the perturbation pressure derived from the linearized Bernoulli and continuity equations. Parameters varied in the analysis include Mach number, mode number and plate size, aspect ratio and mass. The predictions are compared with existing theoretical results and experimental data. The analytical results show that the fluid loading can significantly affect realistic plate responses. Generally, graphite/epoxy and carbon/carbon plates have higher acoustic radiation damping values than similar aluminum plates, except near plate divergence conditions resulting from aeroelastic instability. Universal curves are presented where the acoustic radiation damping normalized by the mass ratio is a linear function of the reduced frequency. A separate curve is required for each Mach number and plate aspect ratio. In addition, acoustic radiation damping values can be greater than or equal to the structural component of the modal critical damping ratio (assumed as 0.01) for the higher subsonic Mach numbers. New experimental data were acquired for comparison with the analytical results.

Lyle, Karen Heitman↗

NASA NTRS2000

Engine System Loads Development for the Fastrac 60K Flight Engine

Early implementation of structural dynamics finite element analyses for calculation of design loads is considered common design practice for high volume manufacturing industries such as automotive and aeronautical industries. However, with the rarity of rocket engine development programs starts, these tools are relatively new to the design of rocket engines. In the new Fastrac engine program, the focus has been to reduce the cost to weight ratio; current structural dynamics analysis practices were tailored in order to meet both production and structural design goals. Perturbation of rocket engine design parameters resulted in a number of Fastrac load cycles necessary to characterize the impact due to mass and stiffness changes. Evolution of loads and load extraction methodologies, parametric considerations and a discussion of load path sensitivities are discussed.

Frady, Greg↗

NASA NTRS2004

Dynamics of Earth orbiting formations

In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange's equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange's equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.

formation flying↗

NASA NTRS2008

Recent Results on the Accurate Measurements of the Dielectric Constant of Seawater at 1.413GHZ

Measurements of the complex. dielectric constant of seawater at 30.00 psu, 35.00 psu and 38.27 psu over the temperature range from 5 C to 3 5 at 1.413 GHz are given and compared with the Klein-Swift results. A resonant cavity technique is used. The calibration constant used in the cavity perturbation formulas is determined experimentally using methanol and ethanediol (ethylene glycol) as reference liquids. Analysis of the data shows that the measurements are accurate to better than 1.0% in almost all cases studied.

Lang, R.H.↗

NASA NTRS2015

The String Stability of a Trajectory-Based Interval Management Algorithm in the Midterm Airspace

NASA's first Air Traffic Management (ATM) Technology Demonstration (ATD-1) was created to facilitate the transition of mature ATM technologies from the laboratory to operational use. The technologies selected for demonstration are the Traffic Management Advisor with Terminal Metering (TMA-TM), which provides precise time-based scheduling in the terminal airspace; Controller Managed Spacing (CMS), which provides terminal controllers with decision support tools enabling precise schedule conformance; and Interval Management (IM), which consists of flight deck automation that enables aircraft to achieve or maintain a precise spacing interval behind a target aircraft. As the percentage of IM equipped aircraft increases, controllers may provide IM clearances to sequences, or strings, of IM-equipped aircraft. It is important for these strings to maintain stable performance. This paper describes an analytic analysis of the string stability of the latest version of NASA's IM algorithm and a fast-time simulation designed to characterize the string performance of the IM algorithm. The analytic analysis showed that the spacing algorithm has stable poles, indicating that a spacing error perturbation will be reduced as a function of string position. The fast-time simulation investigated IM operations at two airports using constraints associated with the midterm airspace, including limited information of the target aircraft's intended speed profile and limited information of the wind forecast on the target aircraft's route. The results of the fast-time simulation demonstrated that the performance of the spacing algorithm is acceptable for strings of moderate length; however, there is some degradation in IM performance as a function of string position.

Swieringa, Kurt A.↗

NASA NTRS1971

Inertial navigation systems analysis.

This volume offers the avionic systems engineer a fundamental exposition of the mechanization and error analysis of inertial navigation systems. While the material is applicable to spacecraft and undersea navigation, emphasis is placed upon terrestrial applications on or slightly above the earth's surface. As a result, practical considerations are geared toward those aircraft navigation systems of particular current interest. Extensive use is made of perturbation techniques to develop linearized system equations, whose solutions closely approximate those obtained by nonlinear differential equations. A unified error analysis technique is developed that is applicable to virtually all system configurations. The technique provides a greatly simplified method for comparing the performance of competing system configurations.

Britting, K. R.↗

NASA NTRS1989

Approximate simulation model for analysis and optimization in engineering system design

Computational support of the engineering design process routinely requires mathematical models of behavior to inform designers of the system response to external stimuli. However, designers also need to know the effect of the changes in design variable values on the system behavior. For large engineering systems, the conventional way of evaluating these effects by repetitive simulation of behavior for perturbed variables is impractical because of excessive cost and inadequate accuracy. An alternative is described based on recently developed system sensitivity analysis that is combined with extrapolation to form a model of design. This design model is complementary to the model of behavior and capable of direct simulation of the effects of design variable changes.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1991

Role of artificial viscosity in Euler and Navier-Stokes solvers

A method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the Navier-Stokes equations. The stability and growth of small perturbations about a steady flow over airfoils are analyzed for various amounts of artificial viscosity. The eigenvalues were determined for a small time-dependent perturbation about a steady inviscid flow over an NACA 0012 airfoil at a Mach number of 0.8 and angle of attack of 0 deg. The method has been applied to inviscid flows here, but as discussed is also applicable to viscous flows. The movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied. The stability boundaries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time-marching scheme are also presented. The eigenvalue procedure not only allows for determining the effect of varying amounts of artificial viscosity, but also for the effects of different forms of artificial viscosity.

Mahajan, Aparajit J.↗

NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗

NASA NTRS1986

An adaptive guidance algorithm for an aerodynamically assisted orbital plane change maneuver

Using analysis results from the post trajectory optimization program, an adaptive guidance algorithm is developed to compensate for density, aerodynamic and thrust perturbations during an atmospheric orbital plane change maneuver. The maneuver offers increased mission flexibility along with potential fuel savings for future reentry vehicles. Although designed to guide a proposed NASA Entry Research Vehicle, the algorithm is sufficiently generic for a range of future entry vehicles. The plane change analysis provides insight suggesting a straight-forward algorithm based on an optimized nominal command profile. Bank angle, angle of attack, and engine thrust level, ignition and cutoff times are modulated to adjust the vehicle's trajectory to achieve the desired end-conditions. A performance evaluation of the scheme demonstrates a capability to guide to within 0.05 degrees of the desired plane change and five nautical miles of the desired apogee altitude while maintaining heating constraints. The algorithm is tested under off-nominal conditions of + or -30% density biases, two density profile models, + or -15% aerodynamic uncertainty, and a 33% thrust loss and for various combinations of these conditions.

Blissit, J. A.↗

NASA NTRS1986

Asymptotic analysis of corona discharge from thin electrodes

The steady discharge of a high-voltage corona is analyzed as a singular perturbation problem. The small parameter is the ratio of the length of the ionization region to the total gap length. By this method, current versus voltage characteristics can be calculated analytically.

Durbin, P. A.↗

NASA NTRS2001

Seismic Study of the Dynamics of the Solar Subsurface from SoHO Observations

In collaboration with Dr. Baudin, we have developed and refined the new observational methodology for local helioseismology known as time-distance analysis. Global helioseismology study the solar oscillations as a superposition of resonant modes, whose properties (mode frequencies) reflect the global structure of the sun (sound speed stratification, rotation rate, etc). In contrast, local helioseismology look at the solar oscillations as wave packets whose propagation will be affected by perturbations of the media sampled. These local perturbations (sound speed or velocity flows) will modify the propagation time, that in turn can be used as a diagnostic tool for a given region. From a data reduction perspective, the processing of solar dopplergrams that result in time-distance maps, i.e. propagation times as a function of distance between bounces at the surface, is radically different from the methodology used for global mode analysis. We have, in a first step, further develop the programs needed to carry out such analysis. We have then applied them to NMI data set, and explore the trade-off between various averaging and filtering approaches - steps required to improve the signal-to-noise ratio of correlation maps - and the resulting stability and precision of the fitted propagation times. While excessive averaging (whether over space, propagation distance, or time) will reduce the diagnostic potential of the method, insufficient averaging lead to unstable fits, or uncertainties so large as to hide the information we seek. In a second phase, we have developed the analysis methodology required to infer local properties from perturbation in time propagation. Namely, we have developed time-distance inversion techniques, with an emphasis on inferences of velocity flows from time anomalies. Note also that during the period covered by this grant, all the investigators on this proposal (i.e., Drs. Baudin, Eff-Darwich, Korzennik, and Noyes) took part in the organization of the SOHO 6 /GONG 99 Workshop: Structure and Dynamics of the Interior of the Sun and Sunlike Stars, held on June 1-4 1999 at the Boston Park Plaza Hotel in Boston, Massachusetts, USA. it was very well attended by more than 160 participants from 26 countries from all over the world. The proceedings were published in two volumes as ESA SP-418, with Sessions I-III in Volume 1, and Sessions IV-VI in Volume 2 (1,000 pages in total). The complete contents are also included in digital form on a CD-ROM included with Volume 1. This CD-ROM also contains additional multi-media material that complements some of the contributions.

Korzennik, Sylvain G.↗

NASA NTRS1989

Influence of non steady gravity on natural convection during micro-gravity solidification of semiconductors. I - Time scale analysis. II - Implications for crystal growth experiments

Consideration is given to the influence of temporal variations in the magnitude of gravity on natural convection during unidirectional solidification of semiconductors. It is shown that the response time to step changes in g at low Rayleigh numbers is controlled by the momentum diffusive time scale. At higher Rayleigh numbers, the response time to increases in g is reduced because of inertial effects. The degree of perturbation of flow fields by transients in the gravitational acceleration on the Space Shuttle and the Space Station is determined. The analysis is used to derive the requirements for crystal growth experiments conducted on low duration low-g vehicles. Also, the effectiveness of sounding rockets and KC-135 aircraft for microgravity experiments is examined.

Griffin, P. R.↗

NASA NTRS1974

On the accuracy of Whitham's method

The steady flow of an ideal gas past a conical body is studied by the method of matched asymptotic expansions and by Whitham's method in order to assess the accuracy of the latter. It is found that while Whitham's method does not yield a correct asymptotic representation of the perturbation field to second order in regions where the flow ahead of the Mach cone of the apex is disturbed, it does correctly predict the changes of the second-order perturbation quantities across a shock (the first-order shock strength). The results of the analysis are illustrated by a special case of a flat, rectangular plate at incidence.

Zahalak, G. I.↗

NASA NTRS1976

Determination of the interaction impedance of coupled cavity slow wave structures

The interaction impedance of coupled cavity slow wave structures can be measured by perturbing the resonances of a shorted length of the structure using a dielectric rod. An analysis of this procedure is presented. The analysis retains radial as well as axial electric fields and all significant space harmonics. The results obtained are easily programmed formulas for calculating total interaction impedance or Pierce impedance using the experimental data.

Connolly, D. J.↗

NASA NTRS1976

Toward the correctable-interference transonic wind tunnel

The concept of a correctable-interference transonic wind tunnel combining a capability for wall-interference assessment with a limited capability for wall control is introduced. Recent progress toward achieving the interference assessment capability is described. The feasibility of using experimentally measured data directly as boundary values for the assessment in lieu of more generally formulated but less accurate wall boundary conditions is demonstrated for two-dimensional subsonic flows. Also, a procedure for transonic analysis of wall interference which leads to a rational definition of the wall-induced perturbation field within the context of nonlinear transonic flow computations is outlined in principle.

Kemp, W. B., Jr.↗

NASA NTRS1979

Tidal interactions in the expanding universe - The formation of prolate systems

The study estimates the magnitude of the anisotropy that can be tidally induced in neighboring initially spherical protostructures, be they protogalaxies, protoclusters, or even uncollapsed density enhancements in the large-scale structure of the universe. It is shown that the linear analysis of tidal interactions developed by Peebles (1969) predicts that the anisotropy energy of a perturbation grows to first order in a small dimensionless parameter, whereas the net angular momentum acquired is of second order. A simple model is presented for the growth of anisotropy by tidal interactions during the nonlinear stage of the development of perturbations. A possible observational test is described of the alignment predicted by the model between the orientations of large-scale perturbations and the positions of neighboring density enhancements.

Binney, J.↗