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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Three-dimensional flow in radial turbomachinery and its impact on design

In the two papers on the 'Theory of Blade Design for Large Deflections' published in 1984, a new inverse design technique was presented for designing the shape of turbomachinery blades in three-dimensional flow. The technique involves the determination of the blade profile from the specification of a distribution of the product of the radius and the pitched averaged tangential velocity (i.e., r bar-V(sub theta), the mean swirl schedule) within the bladed region. This is in contrast to the conventional inverse design technique for turbomachinery blading in two dimensional flow in which the blade surface pressure or velocity distribution is specified and the blade profile determined as a result; this is feasible in two-dimensional flow because the streamlines along the blade surfaces are known a priori. However, in three-dimensional flow, the stream surface is free to deform within the blade passage so that the streamlines on the blade surfaces are not known a priori; thus it is difficult and not so useful to prescribe the blade surface pressure or velocity distribution and determine the resulting blade profile. It therefore seems logical to prescribe the swirl schedule within the bladed region for designing a turbomachinery blade profile in three-dimensional flow. Furthermore, specifying r bar-V(sub theta) has the following advantages: (1) it is related to the circulation around the blade (i.e., it is an aerodynamic quantity); (2) the work done or extracted is approximately proportional to the overall change in r bar-V(sub theta) across a given blade row (Euler turbine equation); and (3) the rate of change of r bar-V(sub theta) along the mean streamline at the blade is related to the pressure jump across the blade and therefore the blade loading. Since the publications of those two papers, the technique has been applied to the design of a low speed as well as a high speed radial inflow turbine (for turbocharger applications) both of which showed definite improvements in performance over that of wheels of conventional designs, the design study of a high pressure ratio radial inflow turbine with and without splitter blades.

Tan, Choon S.↗
NASA NTRS1992

Observations of mode coupling in the solar corona and bipolar noise storms

High-spatial-resolution observations of the sun which reflect on the role of mode coupling in the solar corona, and a number of new observations are presented. It is shown that typically, polarization inversion is seen at 5 GHz in active region sources near the solar limb, but not at 1.5 GHz. Although this is apparently in contradiction to the simplest form of mode coupling theory, it remains consistent with current models for the active region emission. Microwave bursts show no strong evidence for polarization inversion. Bipolar noise storm continuum emission is discussed in some detail, utilizing recent VLA observations at 327 MHz. It is shown that bipolar sources are common at 327 MHz. Further, the trailing component of the bipole is frequently stronger than the leading component, in apparent conflict with the 'leading-spot' hypothesis. The observations indicate that, at 327 MHz, mode coupling is apparently strong at all mode-coupling layers in the solar corona. The 327 MHz observations require a much weaker magnetic field strength in the solar corona to explain this result than did earlier lower-frequency observations: maximum fields are 0.2 G. This is a much weaker field than is consistent with current coronal models.

White, S. M.↗
NASA NTRS1988

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗
NASA NTRS1990

An approximation theory for the identification of nonlinear distributed parameter systems

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Banks, H. T.↗
NASA NTRS1992

An explicit canopy BRDF model and inversion

Based on a rigorous canopy radiative transfer equation, the multiple scattering radiance is approximated by the asymptotic theory, and the single scattering radiance calculation, which requires an numerical intergration due to considering the hotspot effect, is simplified. A new formulation is presented to obtain more exact angular dependence of the sky radiance distribution. The unscattered solar radiance and single scattering radiance are calculated exactly, and the multiple scattering is approximated by the delta two-stream atmospheric radiative transfer model. The numerical algorithms prove that the parametric canopy model is very accurate, especially when the viewing angles are smaller than 55 deg. The Powell algorithm is used to retrieve biospheric parameters from the ground measured multiangle observations.

Liang, Shunlin↗
NASA NTRS1981

The influence of the interplanetary magnetic field and thermal pressure on the position and shape of the magnetopause

An ellipsoidal model, in which the size of an ellipsoid of revolution with a constant eccentricity is inversely proportional to the sixth root of the stream pressure of the solar wind, is used to represent the location of the dayside magnetopause and to study the influences of the interplanetary magnetic field and thermal pressure on its location. The effects of the IMF and thermal pressure on the location of the magnetopause are calculated analytically by using the Chapman-Ferraro theory. The changes in magnetopause size, shape and orientation caused by including the thermal pressure are inversely proportional to the square of the sonic Mach number of the solar wind and are sufficient to explain the observed slight departure of the magnetotail from the expected aberration due to the earth's orbital motion. The results suggest that little angular momentum is being carried away from the sun by the solar wind.

Zhuang, H. C.↗
NASA NTRS1989

Time-domain imaging

The quest for the highest resolution microwave imaging and principle of time-domain imaging has been the primary motivation for recent developments in time-domain techniques. With the present technology, fast time varying signals can now be measured and recorded both in magnitude and in-phase. It has also enhanced our ability to extract relevant details concerning the scattering object. In the past, the interface of object geometry or shape for scattered signals has received substantial attention in radar technology. Various scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequency swept holography, and the synthetic radar imaging, have two things in common: (1) the physical optic far-field approximation, and (2) the utilization of channels as an extra physical dimension, were also advanced. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The development of time-domain techniques are studied through the theoretical aspects as well as experimental verification. The use of time-domain imaging for space robotic vision applications has been suggested.

Tolliver, C. L.↗
NASA NTRS1994

Surface gravity waves at equilibrium with a steady wind

Observations of wave fields' spatial evolution and of gravity wave spectra S(sub omega) are analyzed on the basis of the data reported by several research groups as well as on a 2-year data set of wind and wave measurements by stationary National Oceanic and Atmospheric Administration buoys near the Hawaiian Islands. We seek to clarify the role of the wave energy advection (with the wave group velocity) in the overall energy balance. This advective transfer appears to be no less important than the local (breaking wave induced) dissipation as a factor of wind-wave equilibrium. The advection is found to manifest itself in the shape of wave spectra by reducing the rate at which the spectra density of the wave energy, S(sub omega approximately omega (exp -p), falls off as the frequency increases away from the spectra peak. This and other conclusions are derived by comparing the field observations with theoretical predictions of the weak turbulence theory for a spatially inhomogeneous, statistically stationary, wave field. The observations also indicate that the typical wave age xi = C(sub 0)/U in the open ocean is much greater than the limiting value 1.2 attributed to the 'fully developed sea.' Although the observed spectra can be approximated by a power law with a single 'effective' exponent, this apparent exponent, p, is found to depend on the wave age. At high xi and at frequencies below the generation range, -p tends to -3 rather than the value of -11/3 predicted by the Zakharov-Zaslavskii theory. This deviation is interpreted as pointing to a nonconservative nature of the inverse cascade, the latter including a leakage of energy to low-wavenumber modes. Dependence of the overall effective exponent on xi is shown to be responsible for variation in the coefficients b, B, c, C appearing in empirical fetch laws, such as xi = C bar-x (exp c) and e = B bar-x (exp B), where bar-x and e are the dimensionless fetch and wave energy, respectively.

Glazman, Roman E.↗
NASA NTRS2000

A Reconfiguration Scheme for Accommodating Actuator Failures in Multi-Input, Multi-Output Flight Control Systems

A multi-input, multi-output reconfigurable flight control system design utilizing a robust controller and an adaptive filter is presented. The robust control design consists of a reduced-order, linear dynamic inversion controller with an outer-loop compensation matrix derived from Quantitative Feedback Theory (QFT). A principle feature of the scheme is placement of the adaptive filter in series with the QFT compensator thus exploiting the inherent robustness of the nominal flight control system in the presence of plant uncertainties. An example of the scheme is presented in a pilot-in-the-loop computer simulation using a simplified model of the lateral-directional dynamics of the NASA F18 High Angle of Attack Research Vehicle (HARV) that included nonlinear anti-wind up logic and actuator limitations. Prediction of handling qualities and pilot-induced oscillation tendencies in the presence of these nonlinearities is included in the example.

Siwakosit, W.↗
NASA NTRS2014

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗
NASA NTRS2004

Assembly of Colloidal Aggregates by Electrohydrodynamic Flow: Kinetic Experiments and Scaling Analysis

Electric fields generate transverse flows near electrodes that sweep colloidal particles into densely packed assemblies. We interpret this behavior in terms of electrohydrodynamic motion stemming from distortions of the field by the particles that alter the body force distribution in the electrode charge polarization layer. A scaling analysis shows how the action of the applied electric field generates fluid motion that carries particles toward one another. The resulting fluid velocity is proportional to the square of the applied field and decreases inversely with frequency. Experimental measurements of the particle aggregation rate accord with the electrohydrodynamic theory over a wide range of voltages and frequencies.

Ristenpart, W. D.↗
NASA NTRS2002

Retrievals of Profiles of Fine And Coarse Aerosols Using Lidar And Radiometric Space Measurements

In couple of years we expect the launch of the CALIPSO lidar spaceborne mission designed to observe aerosols and clouds. CALIPSO will collect profiles of the lidar attenuated backscattering coefficients in two spectral wavelengths (0.53 and 1.06 microns). Observations are provided along the track of the satellite around the globe from pole to pole. The attenuated backscattering coefficients are sensitive to the vertical distribution of aerosol particles, their shape and size. However the information is insufficient to be mapped into unique aerosol physical properties and vertical distribution. Infinite number of physical solutions can reconstruct the same two wavelength backscattered profile measured from space. CALIPSO will fly in formation with the Aqua satellite and the MODIS spectro-radiometer on board. Spectral radiances measured by MODIS in six channels between 0.55 and 2.13 microns simultaneously with the CALIPSO observations can constrain the solutions and resolve this ambiguity, albeit under some assumptions. In this paper we describe the inversion method and apply it to aircraft lidar and MODIS data collected over a dust storm off the coast of West Africa during the SHADE experiment. It is shown that the product of the single scattering albedo, omega, and the phase function, P, for backscattering can be retrieved from the synergism between measurements avoiding a priori hypotheses required for inverting lidar measurements alone. The resultant value of (omega)P(180 deg.) = 0.016/sr are significantly different from what is expected using Mie theory, but are in good agreement with recent results obtained from lidar observations of dust episodes. The inversion is robust in the presence of noise of 10% and 20% in the lidar signal in the 0.53 and 1.06 pm channels respectively. Calibration errors of the lidar of 5 to 10% can cause an error in optical thickness of 20 to 40% respectively in the tested cases. The lidar calibration errors cause degradation in the ability to fit the MODIS data. Therefore the MODIS measurements can be used to identify the calibration problem and correct for it. The CALIPSO-MODIS measurements of the profiles of fine and coarse aerosols, together with CALIPSO measurements of clouds vertical distribution, is expected to be critically important in understanding aerosol transport across continents and political boundaries, and to study aerosol-cloud interaction and its effect on precipitation and global forcing of climate.

Kaufman, Yoram↗
NASA NTRS1989

Spin-lattice relaxation and the calculation of gain, pump power, and noise temperature in ruby

The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.

Lyons, J. R.↗
NASA NTRS1973

A geometric theory for the QR, LU and power iterations.

Consideration of the task of computing the invariant subspaces of a given matrix. For this purpose the LU, QR, treppen and bi-iterations have been presented, used, and studied more or less independently of the old-fashioned power method. Each of these methods generates implicitly a sequence of subspaces which determines the convergence properties of the method. The iterations differ in the way in which a basis is constructed to represent each subspace. This aspect largely determines the usefulness of the method. It is shown that the first four iterations produce exactly the same sequence of subspaces as do direct and inverse iteration started from appropriate subspaces. Their convergence properties are therefore the same, and a complete geometric convergence theory is presented in terms of the power method. It is shown that Hessenberg matrices are associated with ideal starting spaces.

Parlett, B. N.↗
NASA NTRS1976

Correlation between nonequilibrium thermodynamic theory and V-I curves of a thermionic converter

The methods of irreversible thermodynamics are used as a basis for developing a transport theory applicable to thermionic cesium diodes. This theory is applied in describing certain aspects of experimental voltage-current (V-I) characteristic curves of a thermionic diode. Emphasis is placed on the open-circuit voltage and short-circuit current of the V-I curves. Experimental results show that the open-circuit voltage is essentially independent of the interelectrode spacing, whereas the short-circuit current varies inversely with the interelectrode separation. The inverse dependence is in agreement with the results of the present analysis and also with results expected from diffusion theory, which has been used in other analyses. In fact, the theory used in this investigation reduces to diffusion theory under special assumptions. Deviations from diffusion theory, which were found in experimental results, can be accounted for using the theory developed in this paper.

Robinson, L. B.↗
NASA NTRS1977

Does electromagnetic radiation accelerate galactic cosmic rays

The 'reactor' theories of Tsytovich and collaborators (1973) of cosmic-ray acceleration by electromagnetic radiation are examined in the context of galactic cosmic rays. It is shown that any isotropic synchrotron or Compton reactors with reasonable astrophysical parameters can yield particles with a maximum relativistic factor of only about 10,000. If they are to produce particles with higher relativistic factors, the losses due to inverse Compton scattering of the electromagnetic radiation in them outweigh the acceleration, and this violates the assumptions of the theory. This is a critical restriction in the context of galactic cosmic rays, which have a power-law spectrum extending up to a relativistic factor of 1 million.

Eichler, D.↗
NASA NTRS2003

Simplified Formulae System for Resonant Inverse Compton Scattering of a Fast Electron in an Intense Magnetic Field

We present simple analytical formulae for the emission spectrum and total power of a special kind of resonant inverse Compton scattering (RICS) of a relativistic electron in an intense magnetic field. In contrast with the available formulae system, we obtain a markedly simplified one based on the semiclassical quantum theory, which is more understandable for people who are unfamiliar with quantum electrodynamics. We show that the RICS process, under an appropriate 'accommodation condition' derived in this paper, is predominantly much more efficient than the coexistent ordinary inverse Compton scattering, and produces highly beamed high-frequency radiation with moderately good monochromaticity. Our formulae are simple to use - thus offering a lucid physical intuition for the theory - and may find wide applications in hard X-ray and gamma-ray astrophysics.

You, J. H.↗
NASA NTRS1977

Unsteady aerodynamic modeling for arbitrary motions

A study is presented on the unsteady aerodynamic loads due to arbitrary motions of a thin wing and their adaptation for the calculation of response and true stability of aeroelastic modes. In an Appendix, the use of Laplace transform techniques and the generalized Theodorsen function for two-dimensional incompressible flow is reviewed. New applications of the same approach are shown also to yield airloads valid for quite general small motions. Numerical results are given for the two-dimensional supersonic case. Previously proposed approximate methods, starting from simple harmonic unsteady theory, are evaluated by comparison with exact results obtained by the present approach. The Laplace inversion integral is employed to separate the loads into 'rational' and 'nonrational' parts, of which only the former are involved in aeroelastic stability of the wing. Among other suggestions for further work, it is explained how existing aerodynamic computer programs may be adapted in a fairly straightforward fashion to deal with arbitrary transients.

Edwards, J. W.↗