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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗
NASA NTRS1995

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗
NASA NTRS1976

Stability of flow of a thermoviscoelastic fluid between rotating coaxial circular cylinders

The stability problem of thermoviscoelastic fluid flow between rotating coaxial cylinders is investigated using nonlinear thermoviscoelastic constitutive equations due to Eringen and Koh. The velocity field is found to be identical with that of the classical viscous case and the case of the viscoelastic fluid, but the temperature and pressure fields are found to be different. By imposing some physically reasonable mechanical and geometrical restrictions on the flow, and by a suitable mathematical analysis, the problem is reduced to a characteristic value problem. The resulting problem is solved and stability criteria are obtained in terms of critical Taylor numbers. In general, it is found that thermoviscoelastic fluids are more stable than classical viscous fluids and viscoinelastic fluids under similar conditions.

Ghandour, N. N.↗
NASA NTRS1993

A new approach for designing self-organizing systems and application to adaptive control

There is tremendous interest in the design of intelligent machines capable of autonomous learning and skillful performance under complex environments. A major task in designing such systems is to make the system plastic and adaptive when presented with new and useful information and stable in response to irrelevant events. A great body of knowledge, based on neuro-physiological concepts, has evolved as a possible solution to this problem. Adaptive resonance theory (ART) is a classical example under this category. The system dynamics of an ART network is described by a set of differential equations with nonlinear functions. An approach for designing self-organizing networks characterized by nonlinear differential equations is proposed.

Ramamoorthy, P. A.↗
NASA NTRS1993

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback

This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.

Gettman, Chang-Ching LO↗
NASA NTRS1997

Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization

The nonlinear rescaling principle (NRP) consists of transforming the objective function and/or the constraints of a given constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal set of solutions coincides. A nonlinear transformation parameterized by a positive scalar parameter and based on a smooth scaling function is used to transform the constraints. The methods based on NRP consist of sequential unconstrained minimization of the classical Lagrangian for the equivalent problem, followed by an explicit formula updating the Lagrange multipliers. We first show that the NRP leads naturally to proximal methods with an entropy-like kernel, which is defined by the conjugate of the scaling function, and establish that the two methods are dually equivalent for convex constrained minimization problems. We then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy-like proximal methods for convex constrained optimization problems. Special cases of the nonlinear resealing algorithm are presented. In particular a new class of exponential penalty-modified barrier functions methods is introduced.

Polyak, Roman↗
NASA NTRS1974

Quantum mechanical streamlines. I - Square potential barrier

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Hirschfelder, J. O.↗
NASA NTRS2010

Loop Shaping Control Design for a Supersonic Propulsion System Model Using Quantitative Feedback Theory (QFT) Specifications and Bounds

This paper covers the propulsion system component modeling and controls development of an integrated mixed compression inlet and turbojet engine that will be used for an overall vehicle Aero-Propulso-Servo-Elastic (APSE) model. Using previously created nonlinear component-level propulsion system models, a linear integrated propulsion system model and loop shaping control design have been developed. The design includes both inlet normal shock position control and jet engine rotor speed control for a potential supersonic commercial transport. A preliminary investigation of the impacts of the aero-elastic effects on the incoming flow field to the propulsion system are discussed, however, the focus here is on developing a methodology for the propulsion controls design that prevents unstart in the inlet and minimizes the thrust oscillation experienced by the vehicle. Quantitative Feedback Theory (QFT) specifications and bounds, and aspects of classical loop shaping are used in the control design process. Model uncertainty is incorporated in the design to address possible error in the system identification mapping of the nonlinear component models into the integrated linear model.

Connolly, Joseph W.↗
NASA NTRS1986

Criteria of chaos in non-linear mechanics

Analytical criteria are derived for the geometrical interpretation (Zak, 1985) of the transition to chaos in nonlinear mechanical systems. The concept of orbital instability in configuration space is employed in the analysis, and the differences between chaotic instability and classical Liapunov instability are explored. The case of a symmetric rigid body rotating about its center of gravity is considered as an example, and the applicability of the present approach to noninertial motion or to continua is discussed.

Zak, M.↗
NASA NTRS1988

Numerical solution methods for viscoelastic orthotropic materials

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Gramoll, K. C.↗
NASA NTRS2001

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Yee, Helen C.↗
NASA NTRS1982

Development of a reduced basis technique for transient thermal analysis

A technique to reduce the degrees of freedom in static and dynamic problems, the reduced basis method, is described. The method combines the classical Rayleigh-Ritz approximation with contemporary finite element methods to retain modeling versatility as the degrees of freedom are reduced. Applications to a nonlinear dynamic response problem are discussed efforts to apply the method to nonlinear transient thermal response problems are summarized. The selection of basis vectors for reducing the system of equations is addressed.

Shore, C. P.↗
NASA NTRS1992

Quantum spatial propagation of squeezed light in a degenerate parametric amplifier

Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.

Deutsch, Ivan H.↗
NASA NTRS2001

Sound Emission of Rotor Induced Deformations of Generator Casings

The casing of large electrical generators can be deformed slightly by the rotor's magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analysed analytically and numerically. From the deformation of the casing, the normal velocity of the generator's surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is round in terms of the Hankel function of second order. The normal velocity or the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated In a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are In excellent agreement with the analytical solution.

Polifke, W.↗
NASA NTRS2012

The Effect of Systematic Error in Forced Oscillation Testing

One of the fundamental problems in flight dynamics is the formulation of aerodynamic forces and moments acting on an aircraft in arbitrary motion. Classically, conventional stability derivatives are used for the representation of aerodynamic loads in the aircraft equations of motion. However, for modern aircraft with highly nonlinear and unsteady aerodynamic characteristics undergoing maneuvers at high angle of attack and/or angular rates the conventional stability derivative model is no longer valid. Attempts to formulate aerodynamic model equations with unsteady terms are based on several different wind tunnel techniques: for example, captive, wind tunnel single degree-of-freedom, and wind tunnel free-flying techniques. One of the most common techniques is forced oscillation testing. However, the forced oscillation testing method does not address the systematic and systematic correlation errors from the test apparatus that cause inconsistencies in the measured oscillatory stability derivatives. The primary objective of this study is to identify the possible sources and magnitude of systematic error in representative dynamic test apparatuses. Sensitivities of the longitudinal stability derivatives to systematic errors are computed, using a high fidelity simulation of a forced oscillation test rig, and assessed using both Design of Experiments and Monte Carlo methods.

Williams, Brianne Y.↗
NASA NTRS2005

Advanced Small Perturbation Potential Flow Theory for Unsteady Aerodynamic and Aeroelastic Analyses

An advanced small perturbation (ASP) potential flow theory has been developed to improve upon the classical transonic small perturbation (TSP) theories that have been used in various computer codes. These computer codes are typically used for unsteady aerodynamic and aeroelastic analyses in the nonlinear transonic flight regime. The codes exploit the simplicity of stationary Cartesian meshes with the movement or deformation of the configuration under consideration incorporated into the solution algorithm through a planar surface boundary condition. The new ASP theory was developed methodically by first determining the essential elements required to produce full-potential-like solutions with a small perturbation approach on the requisite Cartesian grid. This level of accuracy required a higher-order streamwise mass flux and a mass conserving surface boundary condition. The ASP theory was further developed by determining the essential elements required to produce results that agreed well with Euler solutions. This level of accuracy required mass conserving entropy and vorticity effects, and second-order terms in the trailing wake boundary condition. Finally, an integral boundary layer procedure, applicable to both attached and shock-induced separated flows, was incorporated for viscous effects. The resulting ASP potential flow theory, including entropy, vorticity, and viscous effects, is shown to be mathematically more appropriate and computationally more accurate than the classical TSP theories. The formulaic details of the ASP theory are described fully and the improvements are demonstrated through careful comparisons with accepted alternative results and experimental data. The new theory has been used as the basis for a new computer code called ASP3D (Advanced Small Perturbation - 3D), which also is briefly described with representative results.

Batina, John T.↗
NASA NTRS2011

Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging

The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.

coherence theory↗
NASA NTRS2017

Evaluating the Stability of NASA's Space Launch System with Adaptive Augmenting Control

NASA's baseline Space Launch System (SLS) flight control system (FCS) design includes an adaptive augmenting control (AAC) component that modifies the attitude control system response to provide the classical gain-scheduled control architecture with additional performance and robustness. The NASA Engineering and Safety Center (NESC) teamed with the Space Launch System (SLS) Program to perform a comprehensive assessment of the stability and robustness of the FCS with AAC. This paper provides an overview of the approach, specific analysis techniques, and outcomes that were particularly relevant for the SLS Program. Multiple analysis techniques that specifically target the nonlinear AAC were commissioned as part of this assessment, which was completed outside of the Program's standard design analysis cycle. The following analyses were included, with each technique adding its own valuable insights: Lyapunov-based stability analysis, classical stability analysis with static AAC gain variations, circle criterion-based analysis of the FCS with a time-varying element, time-domain stability margin assessment, Monte Carlo simulations with expanded dispersions, and an extensive set of stressing cases. Several of the completed analyses focused on determining whether the inclusion of AAC introduced risk to the FCS, while others quantified the benefits of the adaptive augmentation.

Tannen S Vanzwieten↗