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NASA NTRS1976

Laser absorption phenomena in flowing gas devices

A theoretical and experimental investigation is presented of inverse Bremsstrahlung absorption of CW CO2 laser radiation in flowing gases seeded with alkali metals. In order to motivate this development, some simple models are described of several space missions which could use laser powered rocket vehicles. Design considerations are given for a test call to be used with a welding laser, using a diamond window for admission of laser radiation at power levels in excess of 10 kW. A detailed analysis of absorption conditions in the test cell is included. The experimental apparatus and test setup are described and the results of experiments presented. Injection of alkali seedant and steady state absorption of the laser radiation were successfully demonstrated, but problems with the durability of the diamond windows at higher powers prevented operation of the test cell as an effective laser powered thruster.

Chapman, P. K.↗

NASA NTRS1996

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗

NASA NTRS1985

MAGSAT satellite magnetic anomaly map over South America

A scalar magnetic anomaly map was prepared for South America and adjacent marine areas directly from original MAGSAT orbits. Special problems associated with the separation of external field and crustal anomalies, and the reduction of data to a common altitude are addressed. External fields are manifested in a long-wavelength ring current effect, a medium-wavelength equatorial electrojet, and short-wavelength noise. The noise is reduced by selecting profiles from quiet periods (Kp or = 3), and the effect of the electrojet is minimized by drawing the data set from dawn profiles only. The ring current is corrected through the use of a standard equation, augmented by further digital band-pass filtering. Profiles thus filtered differ primarily in amplitude due solely to satellite altitude differences. These differences are normalized by an inversion of the profile data onto a grid of equivalent point dipoles, and recalculated at an altitude of 350 km. The low altitudes in the study area cause instability in the inversion, necessitating separate inversions of several sub-areas which are subsequently merged. Crustal anomalies reduced-to-the-pole exhibit marked correlations to known tectonic features.

Ridgway, J. R.↗

NASA NTRS1984

An investigation of the consistency of the ionospheric measurements of the photoelectron flux and solar EUV flux

This paper demonstrates that there is an inconsistency between ionospheric measurements of the photoelectron flux and the solar EUV flux. The problem which occurs for EUV wavelengths near 250 A or photoelectron energies near 35 eV has serious implications for theoretical photoelectron flux calculations and could help to explain up to 40 percent of the difference between calculated and measured photoelectron fluxes for electron energies below 35 eV. It is also shown that: (1) only photons with wavelengths shorter than 310 A are of importance in producing photoelectrons; (2) above 20 eV, the photoelectron flux is controlled by the production of primary photoelectrons, while below 20 eV the flux is controlled by degraded photoelectrons; (3) the calculated cascading production rate is insensitive to the cross sections used for the calculation; and (4) the photoelectron flux is inversely proportional to the total inelastic cross sections.

Richards, P. G.↗

NASA NTRS1992

Analytical multiple scattering correction to the Mie theory: Application to the analysis of the lidar signal

The contribution of the multiple scattering to the lidar signal is dependent on the optical depth tau. Therefore, the radar analysis, based on the assumption that the multiple scattering can be neglected is limited to cases characterized by low values of the optical depth (tau less than or equal to 0.1) and hence it exclude scattering from most clouds. Moreover, all inversion methods relating lidar signal to number densities and particle size must be modified since the multiple scattering affects the direct analysis. The essential requests of a realistic model for lidar measurements which include the multiple scattering and which can be applied to practical situations follow. (1) Requested are not only a correction term or a rough approximation describing results of a certain experiment, but a general theory of multiple scattering tying together the relevant physical parameter we seek to measure. (2) An analytical generalization of the lidar equation which can be applied in the case of a realistic aerosol is requested. A pure analytical formulation is important in order to avoid the convergency and stability problems which, in the case of numerical approach, are due to the large number of events that have to be taken into account in the presence of large depth and/or a strong experimental noise.

Flesia, C.↗

NASA NTRS1992

Multi-point inverse design of an infinite cascade of airfoils

This paper describes a practical method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping, and as a result it allows for multi-point design. The cascade blade to be determined is divided into a desired number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distribution is to be achieved. In this way multi-point design requirements can be met. It is necessary to satisfy several conditions that arise to guarantee compatibility with the inlet and outlet flow as well as closure of the cascade blade. Satisfaction of these conditions does not necessarily result in a cascade with all the desired characteristics. For example, the cascade blades may be bulbous or crossed. Through Newton iteration, however, the desired characteristics may be prescribed by allowing for the adjustment of the design parameters that define the mathematical problem through conformal mapping. Several examples will be illustrated to demonstrate the capability of the method. It will be shown that the method is limited to the design of cascades with solidities of up to one.

Selig, Michael S.↗

NASA NTRS2001

Computationally efficient control allocation

A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

Durham, Wayne↗

NASA NTRS2024

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

Yang Zhang↗

NASA NTRS2005

3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.

Anne Douglass↗

NASA NTRS1978

One-dimensional outgassing problem

A predominantly numerical study, using the direct-simulation Monte Carlo method, of the flow from outgassing surfaces with plane, cylindrical, or spherical geometry is presented. The numerical results for the plane flow case are compared with existing theoretical and experimental results and also with a new formulation of the jump conditions across the Knudsen layer between the surface and the continuum outflow. This outflow is sonic for the free expansion case but subsonic in the presence of back-pressure effects. The self-scattered return flux is 19% of the outgassed flux in the sonic outflow case and increases at lower Mach numbers. Thermal accomodation and reflection of this return flux produces an outgassing cooling effect. The cylindrical and spherical geometries introduce an additional Knudsen number defined by the ratio of the mean free path in the effusing gas to the radius. The plane flow results apply when this Knudsen number is less than 0.001 and, when it is of order unity or above, the return flux is inversely proportional to it.

Tran Cong, T.↗

NASA NTRS1991

A new method for analyzing IRAS data to determine the dust temperature distribution

In attempting to analyze the four-band IRAS images of interstellar dust emission, it is found that an inversion theorem recently developed by Chen (1990) enables distribution of the dust to be determined as a function of temperature and thus the total dust column density, for each line of sight. The method and its application to a hypothetical IRAS data set created by assuming a power-law dust temperature distribution, which is characteristic of the actual IRAS data for the Monoceros R2 cloud, are reported. To use the method, the wavelength dependence of the dust emissivity is assumed and a simple function is fitted to the four intensity-wavelength data points. The method is shown to be very successful at retrieving the dust temperature distribution in this case and is expected to have wide applicability to astronomical problems of this type.

Xie, Taoling↗

NASA NTRS1990

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

The stability of spectral approximations to scalar hyperbolic initial-boundary value problems with variable coefficients are studied. Time is discretized by explicit multi-level or Runge-Kutta methods of order less than or equal to 3 (forward Euler time differencing is included), and spatial discretizations are studied by spectral and pseudospectral approximations associated with the general family of Jacobi polynomials. It is proved that these fully explicit spectral approximations are stable provided their time-step, delta t, is restricted by the CFL-like condition, delta t less than Const. N(exp-2), where N equals the spatial number of degrees of freedom. We give two independent proofs of this result, depending on two different choices of approximate L(exp 2)-weighted norms. In both approaches, the proofs hinge on a certain inverse inequality interesting for its own sake. The result confirms the commonly held belief that the above CFL stability restriction, which is extensively used in practical implementations, guarantees the stability (and hence the convergence) of fully-explicit spectral approximations in the nonperiodic case.

Gottlieb, David↗

NASA NTRS1991

The CFL condition for spectral approximations to hyperbolic initial-boundary value problems

Gottlieb, David↗

NASA NTRS2004

Applications of Response Surface-Based Methods to Noise Analysis in the Conceptual Design of Revolutionary Aircraft

Due to the growing problem of noise in today's air transportation system, there have arisen needs to incorporate noise considerations in the conceptual design of revolutionary aircraft. Through the use of response surfaces, complex noise models may be converted into polynomial equations for rapid and simplified evaluation. This conversion allows many of the commonly used response surface-based trade space exploration methods to be applied to noise analysis. This methodology is demonstrated using a noise model of a notional 300 passenger Blended-Wing-Body (BWB) transport. Response surfaces are created relating source noise levels of the BWB vehicle to its corresponding FAR-36 certification noise levels and the resulting trade space is explored. Methods demonstrated include: single point analysis, parametric study, an optimization technique for inverse analysis, sensitivity studies, and probabilistic analysis. Extended applications of response surface-based methods in noise analysis are also discussed.

Hill, Geoffrey A.↗

NASA NTRS1994

Experiments on the flow field physics of confluent boundary layers for high-lift systems

The use of sub-scale wind tunnel test data to predict the behavior of commercial transport high lift systems at in-flight Reynolds number is limited by the so-called 'inverse Reynolds number effect'. This involves an actual deterioration in the performance of a high lift device with increasing Reynolds number. A lack of understanding of the relevant flow field physics associated with numerous complicated viscous flow interactions that characterize flow over high-lift devices prohibits computational fluid dynamics from addressing Reynolds number effects. Clearly there is a need for research that has as its objective the clarification of the fundamental flow field physics associated with viscous effects in high lift systems. In this investigation, a detailed experimental investigation is being performed to study the interaction between the slat wake and the boundary layer on the primary airfoil which is known as a confluent boundary layer. This little-studied aspect of the multi-element airfoil problem deserves special attention due to its importance in the lift augmentation process. The goal of this research is is to provide an improved understanding of the flow physics associated with high lift generation. This process report will discuss the status of the research being conducted at the Hessert Center for Aerospace Research at the University of Notre Dame. The research is sponsored by NASA Ames Research Center under NASA grant NAG2-905. The report will include a discussion of the models that have been built or that are under construction, a description of the planned experiments, a description of a flow visualization apparatus that has been developed for generating colored smoke for confluent boundary layer studies and some preliminary measurements made using our new 3-component fiber optic LDV system.

Nelson, Robert C.↗

NASA NTRS2003

Multi-Decadal Pathfinder Data Sets of Global Land Biophysical Variables from AVHRR and MODIS and their Use in GCM Studies of Biogeophysics and Biogeochemistry

The problem of how the scale, or spatial resolution, of reflectance data impacts retrievals of vegetation leaf area index (LAI) and fraction absorbed photosynthetically active radiation (PAR) has been investigated. We define the goal of scaling as the process by which it is established that LAI and FPAR values derived from coarse resolution sensor data equal the arithmetic average of values derived independently from fine resolution sensor data. The increasing probability of land cover mixtures with decreasing resolution is defined as heterogeneity, which is a key concept in scaling studies. The effect of pixel heterogeneity on spectral reflectances and LAI/FPAR retrievals is investigated with 1 km Advanced Very High Resolution Radiometer (AVHRR) data aggregated to different coarse spatial resolutions. It is shown that LAI retrieval errors at coarse resolution are inversely related to the proportion of the dominant land cover in such pixel. Further, large errors in LAI retrievals are incurred when forests are minority biomes in non-forest pixels compared to when forest biomes are mixed with one another, and vice-versa. A physically based technique for scaling with explicit spatial resolution dependent radiative transfer formulation is developed. The successful application of this theory to scaling LAI retrievals from AVHRR data of different resolutions is demonstrated

Myneni, Ranga↗

NASA NTRS1994

Behavior of an inversion-based precipitation retrieval algorithm with high-resolution AMPR measurements including a low-frequency 10.7-GHz channel

A microwave-based, profile-type precipitation retrieval algorithm has been used to analyze high-resolution passsive microwave measurements over an ocean background, obtained by the Advanced Microwave Precipitation Radiometer (AMPR) flown on a NASA ER-2 aircraft. The analysis is designed to first determine the improvements that can be gained by adding brightness temperature information from the AMPR low-frequency channel (10.7 GHz) to a multispectral retrieval algorithm nominally run with satellite information at 19, 37, and 85 GHz. The impact of spatial resolution degradation of the high-resolution brightness temperature information on the retrieved rain/cloud liquid water contents and ice water contents is then quantified in order to assess the possible biases inherent to satellite-based retrieval. Careful inspection of the high-resolution aircraft dataset reveals five distinctive brightness temperature features associated with cloud structure and scattering effects that are not generally detectable in current passive microwave satellite measurements. Results suggest that the inclusion of 10.7-GHz information overcomes two basic problems associated with three-channel retrieval. Intercomparisons of retrievals carried out at high-resolution and then averaged to a characteristic satellite scale to the corresponding retrievals in which the brightness temperatures are first convolved down to the satellite scale suggest that with the addition of the 10.7-GHz channel, the rain liquid water contents will not be negatively impacted by special resolution degradation. That is not the case with the ice water contents as they appear ti be quite sensitive to the imposed scale, the implication being that as spatial resolution is reduced, ice water contents will become increasingly underestimated.

Smith, E. A.↗

NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗