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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

The Thin Oil Film Equation

A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.

Brown, James L.↗
NASA NTRS1988

Determination of convergence rates across the Ventura Basin, Southern California, using GPS and historical triangulation

Comparison of angles from historical triangulation observations dating as far back as 1932 with Global Positions System (GPS) measurements taken in 1987 indicates that rapid convergence may be taking place on decade timescales in the central and eastern part of the Ventura basin, an east-west trending trough bounded by thrust faults. Changes in angles over this time were analyzed using Prescott's modified Frank's method and in terms of a model which assumes that the regions to the north and south of the basin are rigid blocks undergoing relative motion. For the two block model, inversion of the observed angle changes over the last 28 years for the relative motion vector leads to north-south convergence across the basin of 30 + or - 5 mm/yr, with a left lateral component of 10 + or - 1 mm/yr in the Fillmore-Santa Paula area in the central part of the basin. The modified Frank's method yields strain rates of approximately 2 microrad/yr in both the east and central parts of the basin for measurements spanning the 1971 San Fernando earthquake. Assuming no east-west strain yeilds north-south compression of approximately 3.5 + or - .2 cm/yr. Comparison of triangulation data prior to the earthquake shows no strain outside the margin of error. The convergence rates determined by geodetic techniques are consistent with geologic observations in the area. Such large geodetic deformation rates, with no apparent near-surface creep on the major thrust, can be understood if these faults become subhorizontal at relatively shallow depths and if the subhorizontal portions of the faults are creeping. An alternative explanation of the large displacement rates might be that the pumping of oil in the vicinity of the benchmarks caused large horizontal motions, although it is unlikely that meter scale horizontal motions are due to oil withdrawal. These and other hypotheses are evaluated to better constrain the tectonics of this active region.

Donnellan, Andrea↗
NASA NTRS1972

The P prime(f) to N(h) inversion problem in ionospheric soundings

A general review is given of the inversion techniques used to derive the ionospheric electron density N as a function of altitude h from group path P versus frequency f measurements obtained by vertical incidence ionospheric sounders. The paper discusses the medium under investigation, the experimental techniques used to obtain the P(f) data, the theoretical considerations leading to the integral equation relating P(f) to N(h), and the assumptions made in the inversion process. The lamination inversion technique is then presented, with special attention given to mathematical difficulties arising from discontinuities in the P(f) function, infinities in the integrand, and in some cases unknown integration limits. Methods outlined for minimizing the uncertainties due to discontinuities include the use of redundant information - that is the two distinct P(f) functions available for a given N(h) profile - and the use of models based on statistical data. Mathematical procedures are discussed that increase significantly the efficiency and accuracy of the required numerical integrations. The accuracy of the inversion technique is deduced by comparing the resulting N(h) profile with N(h) data obtained by simultaneous but independent observations.

Jackson, J. E.↗
NASA NTRS1986

Inversion of limb radiance measurements - An operational algorithm

The limb radiance inversion radiometer (LRIR) and limb infrared monitor of the stratosphere (LIMS) experiments aboard the Nimbus 6 and 7 spacecraft have made observations of infrared emission by CO2, O3, H2O, HNO3, and NO2 at the earth's limb. This paper describes a method by which such measurements can be inverted to give vertical distributions of temperature and mixing ratios as functions of pressure. The simple and efficient approach was successfully applied to the LRIR data and subsequently in the initial assessment of the LIMS data. Inversion of synthetic data indicates the size of the errors to be expected as a result of the assumptions and instrumental errors. Retrievals of measured LIMS radiances are shown as examples and compared to in situ observations. The differences are comparable to those obtained with the more complex retrieval scheme used to process the LIMS archival products. Some problems are noted.

Bailey, P. L.↗
NASA NTRS1966

Low-thrust guidance study Final report

Computer algorithm to determine minimum-time optimal control for continuous low-thrust propulsion systems operating in inverse-square gravity field

GRAVITATIONAL FIELD↗
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.↗
NASA NTRS1981

An approximation for inverse Laplace transforms

Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems.

Lear, W. M.↗
NASA NTRS1980

Retrieval of aerosol size distributions from scattering and extinction measurements in the presence of multiple scattering

A fast technique, based on approximation to atmospheric radiative transfer in the solar aureole, is presented for the retrieval of aerosol size distribution from multispectral measurements of both scattered sky radiance and extinction by aerosol media. In this approximation, it is assumed that for a relatively clear day, the sky radiance is due to single scattering by molecules and aerosols, and to multiple scattering by molecules alone. The accuracy of this approximation is discussed in connection with the inversion of scattered radiation data. Results for aerosol size distributions retrieved from multispectral solar extinction measurements by the nonlinear least squares method are discussed, and the retrievals are found to be accurate when checked against ground truth measurements.

Deepak, A.↗
NASA NTRS1986

On compactness of admissible parameter sets: Convergence and stability in inverse problems for distributed parameter systems

A series of numerical examples is reported and several algorithms compared for estimation of coefficients in differential equation models. Unconstrained, constrained and Tikhonov regularization methods are tested for their behavior with regard to both convergence (of approximation methods for the states and parameters) and stability (continuity of the estimates with respect to perturbations in the data or observed states).

Banks, H. T.↗
NASA NTRS1986

Connections between conventional and singular-value-based multi-variable flight control system design techniques

It is proposed that frequency-domain multivariable robustness techniques, when combined with classical multivariable procedures, can offer an additional means of evaluating FCS designs. A lateral-directional FCS for an advanced fighter is used as an example. Robustness to unstructured aircraft-input uncertainties is assessed using purely numerical singular-value procedures. Literal approximations for the singular values of the open-loop plant and controller and for the inverse return difference are shown to provide a means of decomposing and diagnosing robustness problems that are insoluble via purely numerical methods.

Mcruer, D. T.↗
NASA NTRS1988

Analysis of a closed-kinematic chain robot manipulator

Presented are the research results from the research grant entitled: Active Control of Robot Manipulators, sponsored by the Goddard Space Flight Center (NASA) under grant number NAG-780. This report considers a class of robot manipulators based on the closed-kinematic chain mechanism (CKCM). This type of robot manipulators mainly consists of two platforms, one is stationary and the other moving, and they are coupled together through a number of in-parallel actuators. Using spatial geometry and homogeneous transformation, a closed-form solution is derived for the inverse kinematic problem of the six-degree-of-freedom manipulator, built to study robotic assembly in space. Iterative Newton Raphson method is employed to solve the forward kinematic problem. Finally, the equations of motion of the above manipulators are obtained by employing the Lagrangian method. Study of the manipulator dynamics is performed using computer simulation whose results show that the robot actuating forces are strongly dependent on the mass and centroid locations of the robot links.

Nguyen, Charles C.↗
NASA NTRS1989

The reduction correction in North America

An inverse Poisson integral technique was used to determine a gravity field on the geoid which, when continued by analytic free space methods to the topographic surface, agrees with the observed field. The computation is performed in three stages, each stage refining the previous solution using data at progressively increasing resolution (1 x 1 deg, 5 x 5', 5/8 x 5/8') from a decreasing area of integration. Reduction corrections are computed at 5/8 x 5/8' granularity by differencing the geoidal and surface values, smoothed by low-pass filtering and sub-sampled at 5' intervals. The 1 x 1 deg averages of the reduction corrections thus obtained for 172 1 x 1 deg squares in western North America are discussed. The 1 x 1 deg mean reduction corrections are predominantly positive, varying from -3 to +15 mgal, with values in excess of 5 mgal for 26 squares. Their mean and rms values are +2.4 and 3.6 mgal respectively and they correlate well with the mean terrain corrections. The mean and rms contributions from the three stages of computation are: 1 x 1 deg stage +0.15 and 0.7 mgal; 5 x 5' stage + 1.0 and 1.6 mgal; and 5/8 x 5/8' stage +1.3 and 1.8 mgal. These results reflect a tendency for the contributions to become larger and more systematically positive as the wavelengths involved become shorter. The results are discussed in terms of two mechanisms; the first is a tendency for the absolute values of both positive and negative anomalies to become larger when continued downwards and, the second, a non-linear rectification, due to the correlation between gravity anomaly and topographic height, which results in the values continued to a level surface being systematically more positive than those on the topography.

Martzen, P. D.↗
NASA NTRS1995

A Bayesian approach to microwave precipitation profile retrieval

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Evans, K. Franklin↗
NASA NTRS1998

High-Accuracy Compact MacCormack-Type Schemes for Computational Aeroacoustics

Using MacCormack-type methods, a new class of highly accurate compact MacCormack-type schemes is derived which does not require a tridiagonal matrix inversion to obtain the spatial derivatives. Two examples are shown, and results of these schemes for three linear and nonlinear CAA Benchmark Problems are presented.

Hixon, R.↗
NASA NTRS1995

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗
NASA NTRS1978

On a numerical solution of the plastic buckling problem of structures

An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic buckling mode shape is determined by a simple inverse iteration process, once the buckling load has been established. Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.

Gupta, K. K.↗
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 NTRS1988

Acoustic propagation in a thermally stratified atmosphere

Acoustic propagation in an atmosphere with a specific form of a 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 solutions have been considered, the primary emphasis has been on solutions of the acoustic wave equation with point source 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.↗