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NASA NTRS1986

Transonic airfoil analysis and design in nonuniform flow

A nonuniform transonic airfoil code is developed for applications in analysis, inverse design and direct optimization involving an airfoil immersed in propfan slipstream. Problems concerning the numerical stability, convergence, divergence and solution oscillations are discussed. The code is validated by comparing with some known results in incompressible flow. A parametric investigation indicates that the airfoil lift-drag ratio can be increased by decreasing the thickness ratio. A better performance can be achieved if the airfoil is located below the slipstream center. Airfoil characteristics designed by the inverse method and a direct optimization are compared. The airfoil designed with the method of direct optimization exhibits better characteristics and achieves a gain of 22 percent in lift-drag ratio with a reduction of 4 percent in thickness.

Chang, J. F.↗

NASA NTRS1985

Recent results on the Venus atmosphere from Pioneer Venus radio occultations

Temperature structure of the Venus atmosphere was derived from radio occultation data collected by the Pioneer Venus spacecraft during seven occultation seasons in the 1978-1983 period. The measurements, which cover latitudes from both poles to the equator from 40 km to 85 km altitudes, show a latitudinal dependence. At latitudes below 45 deg, there is a smooth temperature transition from the troposphere to the mesosphere. Between 60 and 80 deg, in the 'collar cloud' region, a strong temperature inversion (up to 30 K) appears, which disappears again in the polar areas (80-90 deg), where the mesosphere becomes isothermal without inversion. This temperature behavior is related to the persistent circulation pattern, in which a zonal retrograde motion below 45 deg changes gradually to a circumpolar vortex at the 'collar cloud'. A considerable temporal variability was observed in the thermal structure above the tropopause, suggesting a weather-like variability in the persistent circulation pattern.

Kliore, A. J.↗

NASA NTRS1986

New interstellar masers in nonmetastable ammonia

The first astronomical detections of several ammonia inversion transitions involving nonmetastable levels with energies as high as 1090 K above the ground state are reported. The (J, K) = (9, 6) inversion transition shows maser-like emission in the directions of W51, NGC 7538, W49, and DR 21(OH). The NH3 (6, 3) line exhibits similar characteristics in W51 but is seen in absorption in NGC 7538. These are the first definite detections of ammonia masers in space. The intensities and narrow line widths (0.5-1.5 km/s) for the emission features are in contrast to the previously detected broad, weak, nonmetastable lines attributed to thermal emission in these sources. Temporal variability appears to be evident in the (9, 6) emission in W49 over a 4 month period. The highly excited (J, K) = (9, 6) and (6, 3) ammonia lines are found in regions containig compact H II regions and strongly infrared sources with associated H2O and OH masers; i.e., in regions of active star formation.

Madden, S. C.↗

NASA NTRS1986

The effect of power-law body forces on a thermally driven flow between concentric rotating spheres

A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.

Macaraeg, M. G.↗

NASA NTRS1986

A remanent and induced magnetization model of Magsat vector anomalies over the west African craton

Scalar and vector Magsat anomalies over the west African craton are analyzed by forward and inverse models. A forward model of the Man shield is based on Liberia. Induced magnetization contrasts due to sporadic iron-formations and to regional metamorphic rocks, and a contrast in remanent magnetization within the lower crust are included. This combination reproduces the location, magnitude and adopted local zero level of anomalies in the initial Magsat maps. An inverse model of the Reguibat shield estimates the magnetization contrast of its lithosphere, and when magnetism is restricted to shallower than 75 km both shields can be represented by a susceptibility contrast of +0.02. A residual anomaly between the shields involves a relative deficiency of induced magnetization along with other causes.

Toft, P. B.↗

NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗

NASA NTRS1985

Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization

An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.

Singh, S. N.↗

NASA NTRS1987

Recursive Robot-Arm Dynamics via Filtering and Smoothing

Forward and inverse dynamics solved using Kalman filtering and Bryson-Frazier smoothing. Dynamics of serial-link robot arm solved by using recursive techniques from linear filtering and smoothing theory. Solutions of dynamical equations give forces, moments, and accelerations at joints between links, and multilink inertia matrix and its inverse. Theoretical developments lay foundation for use of filtering and smoothing techniques in design of robot controls.

Rodriguez, Guillermo↗

NASA NTRS1986

Lidar measurements of slant visual range

When converting the lidar equation relative to the extinction coefficient and, correspondingly, the visual range, the instability of the solution at the increase of the optical density of the sounding path is encountered. The search for a stable solution has resulted in the appearance of a set of inversion algorithms differing mainly in the manner of assigning the a priori information on the profile sought. A stable algorithm of inversion is suggested and a comparative analysis and experimental verification of some methods of processing the signals at sounding the optically dense atmospheric formations are given.

Balin, Y. S.↗

NASA NTRS1986

Using a laser aureole to invert lidar return

An aureole generated by a laser beam was studied. The strength of the signal redirected towards a sensor high above the surface by a combination of one scattering event in the marine boundary layer (mbl) and one single reflection event from the ocean surface was estimated. A model of mbl aerosol size distributions was used to estimate Mie scattering for a wide range of meteorolocial conditions. The sea surface reflection was determined from a Gaussian model of the wave slopes. These laser aureoles which were estimated over the wide range of conditions and were normalized by the reflected laser light were found to be highly correlated with the optical depth of the boundary layer. By estimating optical depth from the aureole, the Bernoulli-Riccati inversion of lidar return could be constrained and the inversion accuracy improved. A Monte Carlo program was developed to study the laser aureole generated by up to 8 orders of reflection and scattering. The aureole was generated by a narrow, 10 nsec laser pulse at 1.06 microns and measured by a receiver 10 km above the ocean surface. The original theoretical computation compared well with the Monte Carlo method. When multiple scattereffects were included, the normalized aureole was still highly correlated with the mbl optical depth over the range of conditions.

Hooper, W. P.↗

NASA NTRS1987

On determining important aspects of mathematical models: Application to problems in physics and chemistry

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Rabitz, Herschel↗

NASA NTRS1987

Acoustic propagation in a thermally stratified atmosphere

Acoustic propagation in an atmosphere with a specific form of temperature profile has been investigated by analytical means. The temperature profile used is representative of an actual atmospheric profile and contains three free parameters. Both lapse and inversion cases have been considered. Although ray solution have been considered the primary emphasis has been on solutions of the acoustic wave equation with point force where the sound speed varies with height above the ground corresponding to the assumed temperature profile. The method used to obtain the solution of the wave equation is based on Hankel transformation of the wave equation, approximate solution of the transformed equation for wavelength small compared to the scale of the temperature (or sound speed) profile, and approximate or numerical inversion of the Hankel transformed solution. The solution displays the characteristics found in experimental data but extensive comparison between the models and experimental data has not been carried out.

Vanmoorhem, W. K.↗

NASA NTRS1987

Improved VAS regression soundings of mesoscale temperature structure observed during the 1982 atmospheric variability experiment

An Atmospheric Variability Experiment (AVE) was conducted over the central U.S. in the spring of 1982, collecting radiosonde date to verify mesoscale soundings from the VISSR Atmospheric Sounder (VAS) on the GOES satellite. Previously published VAS/AVE comparisons for the 6 March 1982 case found that the satellite retrievals scarcely detected a low level temperature inversion or a mid-tropospheric cold pool over a special mesoscale radiosonde verification network in north central Texas. The previously published regression and physical retrieval algorithms did not fully utilize VAS' sensitivity to important subsynoptic thermal features. Therefore, the 6 March 1982 case was reprocessed adding two enhancements to the VAS regression retrieval algorithm: (1) the regression matrix was determined using AVE profile data obtained in the region at asynoptic times, and (2) more optimistic signal-to-noise statistical conditioning factors were applied to the VAS temperature sounding channels. The new VAS soundings resolve more of the low level temperature inversion and mid-level cold pool. Most of the improvements stems from the utilization of asynoptic radiosonde observations at NWS sites. This case suggests that VAS regression soundings may require a ground-based asynoptic profiler network to bridge the gap between the synoptic radiosonde network and the high resolution geosynchronous satellite observations during the day.

Chesters, Dennis↗

NASA NTRS1986

On strategies for inverting remote sensing data

Attention is given to a number of methods for inverting remote sensing data obtained in a variety of astronomical applications. Applications include image restoration, inversion of helioseismological data to obtain the internal rotation rate of stars such as the sun, fitting of spectra (especially thermal line spectra) to grating or other dispersed observed spectra, differential emission measure analysis, and reconstruction of images derived from interferometric observations. The results consider the tradeoff between resolution and variance and the stability properties for each method and propose an inversion stragegy using the available techniques.

Jeffrey, W.↗

NASA NTRS1987

Estimation of canopy parameters of row planted vegetation canopies using reflectance data for only four view directions

A procedure for estimating leaf area index (LAI) and percentage of ground cover (GC) for inhomogeneous row planted vegetation canopies using measurement of canopy reflectance (CR) data for only four directions is presented. This procedure, referred to as 'reconstructive inversion', uses the CR data for these directions to first 'reconstruct' the complete bidirectional surface, which is then used to estimate the canopy parameters using the standard inversion of a CR model technique. The technique has been successfully applied to soybeam and corn canopies in various stages of growth.

Goel, Narendra S.↗

NASA NTRS1986

The ill-posed nature of the satellite temperature retrieval problem and the limits of retrievability

The inverse problem of satellite temperature profile retrieval is well known to be ill-posed. This means that not only is a vertical temperature profile solution not unique, but that two solutions can be very different from each other. A set of atmosphere-like, and true atmospheric examples of significantly dissimilar inverse solutions, were sought and found, using an 11-channel simulated HIRS sounding radiometer. Using the Riemann-Lebesgue Lemma for guidance, it is shown that simultaneous, numerical solutions of an atmospheric character may differ by as much as 10 K between 10-1000 mb. However, an empirical search for dissimilar solutions in the natural atmosphere reveals an extremely low probability of finding two significantly different RAOBs which produce radiance measurements whose differences cannot be resolved by the satellite radiometer. The empirical results are used to derive a first estimate of the limits of retrievability, analogous to the limits of predictability derivable from the ill-posed nature of the numerical weather prediction problem.

Thompson, Owen E.↗

NASA NTRS1986

Mass, heat and freshwater fluxes in the South Indian Ocean

Six hydrographic sections were used to examine the circulation and property fluxes in the South Indian Ocean from 10 to 32 deg S. The calculations were made by applying an inverse method to the data. In the interior of the South Indian Ocean, the geostrophic flow is generally northward. At 18 deg S, the northward interior mass flux is balanced by the southward Ekman mass flux at the surface, whereas at 32 deg S the northward interior mass flux is balanced by the southward mass flux of the Agulhas Current. There is a weak, southward mass flux of 6 x 10 to the 9th kg/s in the Mozambique Channel. The rate of water exchange between the Pacific Ocean and the Indian Ocean is dependent on the choice of the initial reference level used in the inverse calculation. The choice of 1500 m, the depth of the deep oxygen minimum, has led to a flux of water from the Pacific Ocean to the Indian Ocean at a rate of 6.6 x 10 to the 9th kg/s. Heat flux calculations indicate that the Indian Ocean is exporting heat to the rest of the world's oceans at a rate of -0.69 x 10 to the 15th W at 18 deg S and -0.25 x 10 to the 15th W at 32 deg S (negative values being southward).

Fu, Lee-Lueng↗

NASA NTRS1987

A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations

A direct, implicit, numerical solution algorithm, with second-order accuracy in space and time, is constructed for the three-dimensional unsteady incompressible Navier-Stokes equations formulated in terms of velocity and vorticity, using generalized orthogonal coordinates to achieve the accurate solution of complex viscous flow configurations. A numerically stable, efficient, direct inversion procedure is developed for the computationally intensive divergence-curl elliptic velocity problem. This overdetermined partial differential operator is first formulated as a uniquely determined, nonsingular matrix-vector problem; this aspect of the procedure is a unique feature of the present analysis. The three-dimensional vorticity-transport equation is solved by a modified factorization technique which completely eliminates the need for any block-matrix inversions and only scalar tridiagonal matrices need to be inverted. The method is applied to the test problem of the three-dimensional flow within a shear-driven cubical box. Coherent streamwise vortex structures are observed within the steady-state flow at Re = 100.

Osswald, G. A.↗