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NASA NTRS1990

Use of reduced basis technique in the inverse dynamics of large space cranes

The inverse dynamics of adaptive structures used as space cranes can prove computationally expensive in the case of large structures, due to the large number of degrees of freedom involved. Consequently, reduced basis techniques (reduction techniques) are frequently used to reduce the problem size to a time manageable level (for possible use in real time control). A reduced basis technique is proposed which is different from, but related to, the path-derivatives reduction technique. A linearly independent set of deflection n-tuples is used, chosen at the beginning of the time range in which it is wished to reduce the equations, in whose subspace it is assumed that the deflection vectors of the unreduced problem will lie (approximately).

Das, S. K.↗

NASA NTRS1993

Study of multi-dimensional radiative energy transfer in molecular gases

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical arrow band model with an exponential-tailed inverse intensity distribution. Consideration of spectral correlation results in some distinguishing features of the Monte Carlo formulations. Validation of the Monte Carlo formulations has been conducted by comparing results of this method with other solutions. Extension of a one-dimensional problem to a multi-dimensional problem requires some special treatments in the Monte Carlo analysis. Use of different assumptions results in different sets of Monte Carlo formulations. The nongray narrow band formulations provide the most accurate results.

Liu, Jiwen↗

NASA NTRS2000

Singular Isothermal Disks: Nonaxiymmetric Bifurcations and Equilibria - Paper 2

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance omega from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M = 2, 3, 4, ... separate bodies. On the basis of our experience in this paper, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Galli, Danielle↗

NASA NTRSDate not supplied

Multi-Wavelength Modeling and Analysis of the Center-to-Limb Effects of Solar Spectroscopy and Helioseismology

An accurate interpretation of observed solar dynamics with different instruments requires modeling solar magnetoconvection indifferent regimes, as well as taking into account center-to-limb effects, magnetic fields, and turbulence. Realistic 3D radiative MHD modeling of the solar magnetoconvection and atmosphere allows us to generate synthetic observables that directly link the physical properties of the solar plasma to spectroscopic and helioseismic observables. In this work, we investigate the influence of the center-to-limb effects for a wide range of wavelengths, which correspond to the operational lines of HMI/SDO, Hinode, DKIST, and other instruments. In particular, we discuss the wavelength-dependency of the center-to-limb helioseismic observations of acoustic travel times that are used for diagnostics of the deep meridional circulation, as well as 'concave' Sun effect. The presented study will support interpretation of helioseismic inversion results by taking into account realistic coupling of subsurface and atmosphere, and geometry-related effects. In particular, it allows us to improve accuracy of solar subsurface measurements from the SoHO and SDO missions, and resolve the long-standing problem of the meridional circulation and evolution with the solar cycle.

SMD↗

NASA NTRSDate not supplied

Minimum-Variance Control Allocation Considering Parametric Model Uncertainty

The control allocation problem was investigated for linear dynamical systems with known parametric uncertainty. Minimizing a cost function that penalizes the variance of the error in achieving commanded forces and moments on the vehicle resulted in a special case of the weighted pseudo-inverse allocator. Rather than an engineer designing the weighting matrix, it is computed from the covariances of the control effectiveness parameters. This minimum-variance allocator balances the effectiveness of the control inputs against the corresponding levels of uncertainty. The approach was demonstrated using simulations of aircraft with realistic uncertainty levels operating in open-loop and closed-loop configurations. Results showed that when model uncertainty is known, significant, and unevenly distributed amongst the controls, the minimum-variance allocator more often achieves the intended forces and moments on the vehicle in comparison to other allocators, which can lead to increased performance, reliability, and safety during flight tests. The cost for this robustness is a diminished achievable moment space for the vehicle.

Control allocation↗

NASA NTRS1977

Study of synthesis techniques for insensitive aircraft control systems

Insensitive flight control system design criteria was defined in terms of maximizing performance (handling qualities, RMS gust response, transient response, stability margins) over a defined parameter range. Wing load alleviation for the C-5A was chosen as a design problem. The C-5A model was a 79-state, two-control structure with uncertainties assumed to exist in dynamic pressure, structural damping and frequency, and the stability derivative, M sub w. Five new techniques (mismatch estimation, uncertainty weighting, finite dimensional inverse, maximum difficulty, dual Lyapunov) were developed. Six existing techniques (additive noise, minimax, multiplant, sensitivity vector augmentation, state dependent noise, residualization) and the mismatch estimation and uncertainty weighting techniques were synthesized and evaluated on the design example. Evaluation and comparison of these six techniques indicated that the minimax and the uncertainty weighting techniques were superior to the other six, and of these two, uncertainty weighting has lower computational requirements. Techniques based on the three remaining new concepts appear promising and are recommended for further research.

Harvey, C. A.↗

NASA NTRS1985

A review of problems and progress in studies of satellite magnetic anomalies

A review is conducted of studies performed during the Magsat project. The obtained data are considered, taking into account questions of data availability, aspects of orbit attitude determination, ionospheric noise, a field model, and an anomaly field presentation. Models for interpretation are discussed, giving attention to forward modeling, and equivalent layer inverse modeling. In an evaluation of rock property constraints, the magnetic bottom is discussed along with Curie points, metamorphism and magnetization, and the direction of magnetization.

Mayhew, M. A.↗

NASA NTRS1996

Exponential Formulae and Effective Operations

One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).

Mielnik, Bogdan↗

NASA NTRS2006

A Novel Concept for a Deformable Membrane Mirror for Correction of Large Amplitude Aberrations

Very large, light weight mirrors are being developed for applications in space. Due to launch mass and volume restrictions these mirrors will need to be much more flexible than traditional optics. The use of primary mirrors with these characteristics will lead to requirements for adaptive optics capable of correcting wave front errors with large amplitude relatively low spatial frequency aberrations. The use of low modulus membrane mirrors actuated with electrostatic attraction forces is a potential solution for this application. Several different electrostatic membrane mirrors are now available commercially. However, as the dynamic range requirement of the adaptive mirror is increased the separation distance between the membrane and the electrodes must increase to accommodate the required face sheet deformations. The actuation force applied to the mirror decreases inversely proportional to the square of the separation distance; thus for large dynamic ranges the voltage requirement can rapidly increase into the high voltage regime. Experimentation with mirrors operating in the KV range has shown that at the higher voltages a serious problem with electrostatic field cross coupling between actuators can occur. Voltage changes on individual actuators affect the voltage of other actuators making the system very difficult to control. A novel solution has been proposed that combines high voltage electrodes with mechanical actuation to overcome this problem. In this design an array of electrodes are mounted to a backing structure via light weight large dynamic range flextensional actuators. With this design the control input becomes the separation distance between the electrode and the mirror. The voltage on each of the actuators is set to a uniform relatively high voltage, thus the problem of cross talk between actuators is avoided and the favorable distributed load characteristic of electrostatic actuation is retained. Initial testing and modeling of this concept demonstrates that this is an attractive concept for increasing the dynamic range capability of electrostatic deformable mirrors.

Moore, Jim↗

NASA NTRS2018

Simulation of Sound Absorption by Scattering Bodies Treated with Acoustic Liners Using a Time-Domain Boundary Element Method

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance, Z(w). Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering of geometric bodies treated with acoustic liners. This work uses an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Y(w) = 1/Z(w). An admittance boundary condition will be derived and coupled with a time domain boundary integral equation. The solution will be obtained iteratively using spatial and temporal basis functions and will allow for acoustic scattering problems to be modeled with geometries consisting of both unlined and soft surfaces. Stability will be demonstrated through eigenvalue analysis.

Pizzo, Michelle E.↗

NASA NTRS2002

Towards Resolving the Crab Sigma-Problem: A Linear Accelerator?

Using the exact solution of the axisymmetric pulsar magnetosphere derived in a previous publication and the conservation laws of the associated MHD flow, we show that the Lorentz factor of the outflowing plasma increases linearly with distance from the light cylinder. Therefore, the ratio of the Poynting to particle energy flux, generically referred to as sigma, decreases inversely proportional to distance, from a large value (typically approx. greater than 10(exp 4)) near the light cylinder to sigma approx. = 1 at a transition distance R(sub trans). Beyond this distance the inertial effects of the outflowing plasma become important and the magnetic field geometry must deviate from the almost monopolar form it attains between R(sub lc), and R(sub trans). We anticipate that this is achieved by collimation of the poloidal field lines toward the rotation axis, ensuring that the magnetic field pressure in the equatorial region will fall-off faster than 1/R(sup 2) (R being the cylindrical radius). This leads both to a value sigma = a(sub s) much less than 1 at the nebular reverse shock at distance R(sub s) (R(sub s) much greater than R(sub trans)) and to a component of the flow perpendicular to the equatorial component, as required by observation. The presence of the strong shock at R = R(sub s) allows for the efficient conversion of kinetic energy into radiation. We speculate that the Crab pulsar is unique in requiring sigma(sub s) approx. = 3 x 10(exp -3) because of its small translational velocity, which allowed for the shock distance R(sub s) to grow to values much greater than R(sub trans).

Contopoulos, Ioannis↗

NASA NTRS1980

Transmitted sound field due to an impulsive line acoustic source bounded by a plate followed by a vortex sheet

The propagation of sound due to a line acoustic source in the moving stream across a semiinfinite vortex sheet which trails from a rigid plate is examined in a linear theory for the subsonic case. A solution for the transmitted sound field is obtained with the aid of multiple integral transforms and the Wiener-Hopf technique for both the steady state (time harmonic) and initial value (impulsive source) situations. The contour of inverse transform and hence the decomposition of the functions are determined through causality and radiation conditions. The solution obtained satisfies causality and the full Kutta conditions. The transmitted sound field is composed of two waves in both the stady state and initial value problems. One is the wave scattered from the edge of the plate which is associated with the bow wave and the instability wave. These waves exist in the downstream sectors. The other is the wave transmitted through the vortex sheet which is also associated with the instability wave. Regional divisions of the transmitted sound field are identified.

Miura, T.↗

NASA NTRS1989

Direct method for solution of three-dimensional unsteady incompressible Navier-Stokes equations

A three-dimensional, unsteady analysis for the velocity-vorticity formulation of the Navier-Stokes (NS) equations is described. This formulation highlights the natural separation of the spin dynamics of a fluid particle from its translational kinematics. This separation is exploited to produce a single pass direct inversion of the full unsteady NS operator without the need to iterate either the future wall vorticity or the nonlinear vorticity convection terms. The method has uniform second-order accuracy in time and space. As an example, it is applied to the problem of the three-dimensional flow within a shear-driven cubical box. Results are obtained for Re = 100, 400, and 1000 using a preliminary (25, 25, 25) mesh.

Osswald, G. A.↗

NASA NTRS1994

Development of nonintrusive, scatter-independent techniques for measurement of liquid density inside dense sprays

A nonintrusive optical technique for measuring the liquid density in sprays used to simulate LOX injector flows is under development. This manuscript is a report on work toward that development which is currently in progress. The technique is a scatter-independent, absorption-based approach which depends on the numerical inversion of a collection of absorption profiles. For the case in which visible radiation passes through liquid-gas interfaces so numerous in sprays, substantial reductions and alterations in the signal result from scattering even in the absence of absorption. To avoid these problems, X-Rays will be used as the absorbed radiation. The experimental process is simulated by integrating the absorption spectrum for a known distribution, adding instrument noise to this 'measurement', creating a projection from the 'measurement', filtering the projection, inverting the projection, and comparing the results with the original prescribed distribution.

Hartfield, Roy↗

NASA NTRS1973

Application of Papkovich-Neuber potentials to a crack problem.

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered in this paper. A closed form solution using four harmonic functions is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically.

Kassir, M. K.↗

NASA NTRS1981

Investigations of medium wavelength magnetic anomalies in the eastern Pacific using MAGSAT data

The suitability of using magnetic field measurements obtained by MAGSAT is discussed with regard to resolving the medium wavelength anomaly problem. A procedure for removing the external field component from the measured field is outlined. Various methods of determining crustal magnetizations are examined in light of satellite orbital parameters resulting in the selection of the equivalent source technique for evaluating scalar measurements. A matrix inversion of the vector components is suggested as a method for arriving at a scalar potential representation of the field.

Harrison, C. G. A.↗

NASA NTRS1994

NCAR CCM2 simulation of the modern Antarctic climate

The National Center for Atmospheric Research (NCAR) community climate model version 2 (CCM2) simulation of the circumpolar trough, surface air temperature, the polar vortex, cloudiness, winds, and atmospheric moisture and energy budgets are examined to validate the model's representation of the present-day Antarctic climate. The results show that the CCM2 can well simulate many important climate features over Antarctica, such as the location and intensity of the circumpolar trough, the coreless winter over the plateau, the intensity and horizontal distribution of the surface inversion, the speed and streamline pattern of the katabatic winds, the double jet stream feature over the southern Indian and Pacific oceans, and the arid climate over the continent. However, there are also some serious errors in the model. Some are due to old problems but some are caused by the new parameterizations in the model. The model errors over high southern latitudes can be summarized as follows: The circumpolar trough, the polar vertex, and the westerlies in midlatitudes are too strong; the semiannual cycle of the circumpolar trough is distorted compared to the observations; the low centers of the circumpolar trough and the troughs in the middle and upper troposphere are shifted eastward by 15 deg - 40 deg longitude; the surface temperatures are too cold over the plateau in summer and over the coastline in winter; the polar tropopause continues to have a cold bias; and the cloudiness is too high over the continent. These biases are induced by two major factors: (1) the cloud optical properties in tropical and middle latitudes, which cause the eastward shift of troughs and surface low centers and the error in the semiannual cycle, and (2) the cold bias of the surface air temperature, which is attributed to the oversimulation of cloudiness over the continent, especially during summer, and the uniform 2-m-thick sea ice. The constant thickness of sea ice suppresses the energy flux from the ocean to the atmosphere and hence reduces the air temperature near the coast during winter. Finally, although the simulated Antarctic climate still suffers these biases, the overall performance of the CCM2 is much better than that of the CCM1-T42. Therefore the CCM2 is good enough to be used for climate change studies, especially over Antarctica.

Tzeng, Ren-Yow↗

NASA NTRS1996

Optimum Transonic Airfoils Based on the Euler Equations

We solve the problem of determining airfoils that approximate, in a least square sense, given surface pressure distributions in transonic flight regimes. The flow is modeled by means of the Euler equations and the solution procedure is an adjoint- based minimization algorithm that makes use of the inverse Theodorsen transform in order to parameterize the airfoil. Fast convergence to the optimal solution is obtained by means of the pseudo-time method. Results are obtained using three different pressure distributions for several free stream conditions. The airfoils obtained have given a trailing edge angle.

Iollo, Angelo↗