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NASA NTRS1997

Implicit Kalman filtering

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Non-NASA Center↗

NASA NTRS1995

ANSYS tools in modeling tires

This presentation summarizes the capabilities in the ANSYS program that relate to the computational modeling of tires. The power and the difficulties associated with modeling nearly incompressible rubber-like materials using hyperelastic constitutive relationships are highlighted from a developer's point of view. The topics covered include a hyperelastic material constitutive model for rubber-like materials, a general overview of contact-friction capabilities, and the acoustic fluid-structure interaction problem for noise prediction. Brief theoretical development and example problems are presented for each topic.

Ali, Ashraf↗

NASA NTRS1991

Millimeter-wave integrated-horn antennas. I - Theory. II - Experiment

Full-wave analysis is employed to determine the far-field pattern and input impedance of a dipole-fed horn antenna in a ground plane, and the theoretical results are compared with mm-wave and microwave data. The theoretical work exploits the Green's function corresponding to the horn structure and the method of moments. It is determined that the horn should have 70 sections/wavelength and 50 secondary modes for optimized accuracy, and certain dipole positions can reduce the resonance to zero. The experimentally derived impedance and radiation patterns agree with the constraints developed theoretically. The 70-degree flare-angle horn with selected dipole positions and horn apertures yields good radiation patterns, cross-polarization levels, and resonant dipole impedances. The conclusions are of interest to the development of the horn antennas etched in Si/GaAs for applications to zero-visibility tracking, radio astronomy, plasma diagnostics, and remote sensing.

Eleftheriades, George V.↗

NASA NTRS1997

Proceedings of the Workshop on the Scientific Applications of Clocks in Space

The Workshop on Scientific Applications of Clocks in space was held to bring together scientists and technologists interested in applications of ultrastable clocks for test of fundamental theories, and for other science investigations. Time and frequency are the most precisely determined of all physical parameters, and thus are the required tools for performing the most sensitive tests of physical theories. Space affords the opportunity to make measurement, parameters inaccessible on Earth, and enables some of the most original and sensitive tests of fundamental theories. In the past few years, new developments in clock technologies have pointed to the opportunity for flying ultrastable clocks in support of science investigations of space missions. This development coincides with the new NASA paradigm for space flights, which relies on frequent, low-cost missions in place of the traditional infrequent and high-cost missions. The heightened interest in clocks in space is further advanced by new theoretical developments in various fields. For example, recent developments in certain Grand Unified Theory formalisms have vastly increased interest in fundamental tests of gravitation physics with clocks. The workshop included sessions on all related science including relativity and gravitational physics, cosmology, orbital dynamics, radio science, geodynamics, and GPS science and others, as well as a session on advanced clock technology.

Maleki, Lute↗

NASA NTRS1999

Use of Microgravity to Control the Microstructure of Eutectics

This grant began in June of 1996. Its long term goal is to be able to control the microstructure of directionally solidified eutectic alloys, through an improved understanding of the influence of convection. The primary objective of the projects in the present grant is to test hypotheses for the reported influence of microgravity on the microstructure of eutectics. The prior experimental results on the influence of microgravity on the microstructure of eutectics have been contradictory. With lamellar eutectics, microgravity had a negligible effect on the microstructure. Microgravity experiments with fibrous eutectics sometimes showed a finer microstructure and sometimes a coarser microstructure. Most research has been done on the MnBi/Bi rod-like eutectic. Larson and Pirich obtained a two-fold finer microstructure both from microgravity and by use of a magnetic field to quench buoyancy-driven convection. Smith, on the other hand, observed no change in microgravity. Prior theoretical work at Clarkson University showed that buoyancy-driven convection in the vertical Bridgman configuration is not vigorous enough to alter the concentration field in front of a growing eutectic sufficiently to cause a measurable change in microstructure. We assumed that the bulk melt was at the eutectic composition and that freezing occurred at the extremum, i.e. with minimum total undercooling at the freezing interface. There have been four hypotheses attempting to explain the observed changes in microstructure of fibrous eutectics caused by convection: I .A fluctuating freezing rate, combined with unequal kinetics for fiber termination and branching. 2. Off-eutectic composition, either in the bulk melt due to an off-eutectic feed or at the freezing interface because of departure from the extremum condition. 3. Presence of a strong habit modifying impurity whose concentration at the freezing interface would be altered by convection. At the beginning of the present grant, we favored the first of these hypotheses and set out to test it both experimentally and theoretically. We planned the following approaches: I .Pass electric current pulses through the MnBi/Bi eutectic during directional solidification in order to produce an oscillatory freezing rate. 2. Directionally solidify the MnBi/Bi eutectic on Mir using the QUELD II gradient freeze furnace developed by Professor Smith at Queen's University. 3. Select another fibrous eutectic system for investigation using the Accelerated Crucible Rotation Technique to introduce convection. 4. Develop theoretical models for eutectic solidification with an oscillatory freezing rate. Because of the problems with Mir, we substituted ground-based experiments at Queen's University with QUELD II vertical and horizontal, with and without vibration of the furnace. The Al-Si system was chosen for the ACRT experiments. Three related approaches were used to model eutectic solidification with an oscillatory freezing rate. A sharp interface model was used to calculate composition oscillations at the freezing interface in response to imposed freezing rate oscillations.

Wilcox. William R.↗

NASA NTRS2004

Droplet-Surface Impingement Dynamics for Intelligent Spray Design

Spray cooling has high potential in thermal management and life support systems by overcoming the deleterious effect of microgravity upon two-phase heat transfer. In particular spray cooling offers several advantages in heat flux removal that include the following: 1) By maintaining a wetted surface, spray droplets impinge upon a thin fluid film rather than a dry solid surface; 2. Most heat transfer surfaces will not be smooth but rough. Roughness can enhance conductive cooling, aid liquid removal by flow channeling; and 3. Spray momentum can be used to a) substitute for gravity delivering fluid to the surface, b) prevent local dryout and potential thermal runaway and c) facilitate liquid and vapor removal. Yet high momentum results in high We and Re numbers characterizing the individual spray droplets. Beyond an impingement threshold, droplets splash rather than spread. Heat flux declines and spray cooling efficiency can markedly decrease. Accordingly we are investigating droplet impingement upon a) dry solid surfaces, b) fluid films, c) rough surfaces and determining splashing thresholds and relationships for both dry surfaces and those covered by fluid films. We are presently developing engineering correlations delineating the boundary between splashing and non-splashing regions. Determining the splash/non-splash boundary is important for many practical applications. Coating and cooling processes would each benefit from near-term empirical relations and subsequent models. Such demonstrations can guide theoretical development by providing definitive testing of its predictive capabilities. Thus, empirical relations describing the boundary between splash and non-splash are given for drops impinging upon a dry solid surface and upon a thin fluid film covering a similar surface. Analytical simplification of the power laws describing the boundary between the splash and non-splash regions yields insight into the engineering parameters governing the splash and non-splash outcomes of the fluid droplets. The power law correlation is shown separating the splashing versus non-splashing regions as developed for droplets impinging upon a dry solid surface. Splashing upon a dry surface is reasonably described by Ca greater than 0.85, reflecting the competing roles of surface tension and viscosity. The power law correlation is shown separating the splashing versus non-splashing regions as developed for droplets impinging upon a thin fluid film covering the solid surface. Splashing upon a thin fluid film, as described by v (pd/s) greater than 63, is governed by fluid density and surface tension, but is rather independent of viscosity. Finally, the data presented here suggests that a more direct dependence upon the surface tension and viscosity, given a better understanding of their interplay, would allow accurate description of the droplet-surface impacts for more complicated situations involving non-Newtonian fluids, specifically those exhibiting viscoelastic behavior.

Wal, Randy L. Vander↗

NASA NTRS1985

On thermomechanical testing in support of constitutive equation development for high temperature alloys

Three major categories of testing are identified that are necessary to provide support for the development of constitutive equations for high temperature alloys. These are exploratory, charactrization and verification tests. Each category is addressed and specific examples of each are given. An extensive, but not exhaustive, set of references is provided concerning pertinent experimental results and their relationships to theoretical development. This guide to formulating a meaningful testing effort in support of consitutive equation development can also aid in defining the necessary testing equipment and instrumentation for the establishment of a deformation and structures testing laboratory.

Robinson, D. N.↗

NASA NTRSDate not supplied

Geometric Acoustics for Aircraft Noise Scattering

This paper discusses aircraft noise scattering by geometric acoustics, which consists of the basic features of sound propagation and reflection in rays or ray tubes, diffraction by smooth geometry in terms of surface creeping waves, and diffraction by abrupt geometry features such as the wing trailing edges. Based on the classic theories of these features, prediction methodologies can be constructed for aircraft noise scattering. The methodologies, however, require important modifications and extensions to account for unique features in aircraft noise applications, for both current conventional aircraft and future unconventional designs. These modifications and extensions include the derivation of a general reflection coefficient that contains the effects of surface geometry curvature, surface impedance, and mean flow. Corrections to the basic formulation of diffraction, both smooth geometry and sharp edges, are formulated to account for the finite dimensions of practical applications. For smooth geometry diffraction, a second order correction is used to continuously transition from insolified to shadow zones and an approach is presented to compute the properties of the geodesic path of surface wave propagation. A model is developed to make use of the ray propagation formulation for incoherent and partially coherent propagation and scattering, which is an important phenomenon in aircraft noise. Mean flow effect is also included in the methodology for low Mach number flows. Examples of calculations based on these theoretical developments are presented to illustrate the unique features in aircraft noise applications.

Yueping Guo↗

NASA NTRS1992

The use of cross-section warping functions in composite rotor blade analysis

During the contracted period, our research was concentrated into three areas. The first was the development of an accurate and a computationally efficient method for predicting the cross-section warping functions in an arbitrary cross-section composed of isotropic and/or anisotropic materials. The second area of research was the development of a general higher-order one-dimensional theory for anisotropic beams. The third area of research was the development of an analytical model for assessing the extension-bend-twist coupling behavior of nonhomogeneous anisotropic beams with initial twist. In the remaining six chapters of this report, the three different research areas and associated sub-research areas are covered independently including separate introductions, theoretical developments, numerical results, and references.

Kosmatka, J. B.↗

NASA NTRS1996

Aircraft Interior Noise Control Using Distributed Piezoelectric Actuators

Developing a control system that can reduce the noise and structural vibration at the same time is an important task. This talk presents one possible technical approach for accomplishing this task. The target application of the research is for aircraft interior noise control. The emphasis of the present approach is not on control strategies, but rather on the design of actuators for the control system. In the talk, a theory of distributed piezoelectric actuators is introduced. A uniform cylindrical shell is taken as a simplified model of fuselage structures to illustrate the effectiveness of the design theory. The actuators developed are such that they can reduce the tonal structural vibration and interior noise in a wide range of frequencies. Extensive computer simulations have been done to study various aspects of the design theory. Experiments have also been conducted and the test results strongly support the theoretical development.

Sun, Jian Q.↗

NASA NTRS2018

An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes

Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.

vegetation remote sensing; stochastic radiative tr↗

NASA NTRS2021

Collision Free Dynamic Stability of Formations Using Projection Based Estimators

Transient instability is a phenomenon where inter- agent collisions can occur in dynamically stable formations of autonomous agents. Therefore, the necessity to manage and mitigate transient instabilities is essential for successfully deploying formation structures. This paper develops a novel control architecture that augments the baseline formation maintenance controller to mitigate transient instabilities. At its heart, the proposed architecture consists of a projection operator based estimator disguised as a reference model that generates collision-free trajectories for the agents to follow. This paper’s main theoretical result shows that the proposed control architecture can simultaneously mitigate transient instabilities and guarantee asymptotic convergence of the formation dynamics. Also, an illustrative example demonstrates the theoretical developments presented in this paper.

Bayard, David S.↗

NASA NTRS1985

Probabilistic Finite Element: Variational Theory

The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.

Belytschko, T.↗

NASA NTRS1986

Optical imaging spectroscopy

During the recent solar maximum the combination of imaging and spectroscopy in the visible part of the spectrum became a powerful tool for observational study of flares primarily because of the development of two-dimensional charge-coupled-device (CCD) arrays. In combination with appropriate new operational methods, this has led to the ability to observe, for the first time, the preflare and impulsive-phase physical processes associated with spatially resolved features of flare loops. As a result of concurrent theoretical developments, modeling progressed from an empirical to a physical level. This made it possible to interpret imaging spectra in terms of coronal pressure and heat flux, particle beam heating, chromospheric evaporation, and explosive chromospheric dynamics at the footpoints of flare loops. There is clear potential for further advances in the near future, taking advantage of improvements in digital recording speed (approx. 10-fold), number of photosensitive elements per array (approx. 10-fold), real-time data pre-reduction (potentially 10- to 100-fold), and using multiple CCD arrays. By the time of the next solar maximum imaging spectroscopy is expected to achieve spatial resolution or approx. arc 1 arc s, temporal resolution or approx. 5 s, and simultaneous critically-sampled spectroscopy of several lines and continua. As a result, continued increase in our understanding of the physical processes and configurations of solar flares in the chromosphere, temperature minimum region, and photosphere can be anticipated. Even greater progress toward a more global understanding of flares will obviously come about when simultaneous optical, X-ray, and gamma-ray imaging spectroscopy are possible.

Canfield, R. C.↗

NASA NTRS1986

Advanced natural laminar flow airfoil with high lift to drag ratio

An experimental verification of a high performance natural laminar flow (NLF) airfoil for low speed and high Reynolds number applications was completed in the Langley Low Turbulence Pressure Tunnel (LTPT). Theoretical development allowed for the achievement of 0.70 chord laminar flow on both surfaces by the use of accelerated flow as long as tunnel turbulence did not cause upstream movement of transition with increasing chord Reynolds number. With such a rearward pressure recovery, a concave type deceleration was implemented. Two-dimensional theoretical analysis indicated that a minimum profile drag coefficient of 0.0026 was possible with the desired laminar flow at the design condition. With the three-foot chord two-dimensional model constructed for the LTPT experiment, a minimum profile drag coefficient of 0.0027 was measured at c sub l = 0.41 and Re sub c = 10 x 10 to the 6th power. The low drag bucket was shifted over a considerably large c sub l range by the use of the 12.5 percent chord trailing edge flap. A two-dimensional lift to drag ratio (L/D) was 245. Surprisingly high c sub l max values were obtained for an airfoil of this type. A 0.20 chort split flap with 60 deg deflection was also implemented to verify the airfoil's lift capabilities. A maximum lift coefficient of 2.70 was attained at Reynolds numbers of 3 and 6 million.

Viken, Jeffrey K.↗

NASA NTRS1983

Propagation of solar disturbances - Theories and models

Recent theoretical developments and construction of several models for the propagation of solar disturbances from the sun and their continuation throughout heliospheric space are discussed. Emphasis centers on physical mechanisms as well as mathematical techniques (i.e., analytical and numerical methods). This outline will lead to a discussion of the state-of-the-art of theoretically based modeling efforts in this area. It is shown that the fundamental theory for the study of propagation of disturbances in heliospheric space is centered around the self-consistent analysis of wave and mass motion within the context of magnetohydrodynamics in which the small scale structures will be modified by kinetic effects. Finally, brief mention is made of some interesting problems for which attention is needed for advancement of the understanding of the physics of large scale propagation of solar disturbances in heliospheric space.

Wu, S. T.↗

NASA NTRS1986

Shock waves and shock tubes; Proceedings of the Fifteenth International Symposium, Berkeley, CA, July 28-August 2, 1985

A detailed survey is presented of shock tube experiments, theoretical developments, and applications being carried out worldwide. The discussions explore shock tube physics and the related chemical, physical and biological science and technology. Extensive attention is devoted to shock wave phenomena in dusty gases and other multiphase and heterogeneous systems, including chemically reactive mixtures. Consideration is given to techniques for measuring, visualizing and theoretically modeling flowfield, shock wave and rarefaction wave characteristics. Numerical modeling is explored in terms of the application of computational fluid dynamics techniques to describing flowfields in shock tubes. Shock interactions and propagation, in both solids, fluids, gases and mixed media are investigated, along with the behavior of shocks in condensed matter. Finally, chemical reactions that are initiated as the result of passage of a shock wave are discussed, together with methods of controlling the evolution of laminar separated flows at concave corners on advanced reentry vehicles.

Bershader, D.↗

NASA NTRS1994

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

Bey, Kim S.↗