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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

On the nonlinear development of the most unstable Goertler vortex mode TLSP - Final report

The nonlinear development of the most unstable Goertler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Goertler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Goertler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Goertler equations valid for O(1) Goertler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗
NASA NTRS1998

The NASA-Langley Wake Vortex Modelling Effort in Support of an Operational Aircraft Spacing System

Two numerical modelling efforts, one using a large eddy simulation model and the other a numerical weather prediction model, are underway in support of NASA's Terminal Area Productivity program. The large-eddy simulation model (LES) has a meteorological framework and permits the interaction of wake vortices with environments characterized by crosswind shear, stratification, humidity, and atmospheric turbulence. Results from the numerical simulations are being used to assist in the development of algorithms for an operational wake-vortex aircraft spacing system. A mesoscale weather forecast model is being adapted for providing operational forecast of winds, temperature, and turbulence parameters to be used in the terminal area. This paper describes the goals and modelling approach, as well as achievements obtained to date. Simulation results will be presented from the LES model for both two and three dimensions. The 2-D model is found to be generally valid for studying wake vortex transport, while the 3-D approach is necessary for realistic treatment of decay via interaction of wake vortices and atmospheric boundary layer turbulence. Meteorology is shown to have an important affect on vortex transport and decay. Presented are results showing that wake vortex transport is unaffected by uniform fog or rain, but wake vortex transport can be strongly affected by nonlinear vertical change in the ambient crosswind. Both simulation and observations show that atmospheric vortices decay from the outside with minimal expansion of the core. Vortex decay and the onset three-dimensional instabilities are found to be enhanced by the presence of ambient turbulence.

Proctor, Fred H.↗
NASA NTRSDate not supplied

RESIDUAL DEFORMATION ANALYSIS IN COMPOSITE SHELL STRUCTURES MANUFACTURED USING AUTOMATED FIBER PLACEMENT

The manufacturing of composites typically produces residual stresses that can significantly affect the final shape of the structure. The process of automated fiber placement (AFP) has become a prominent manufacturing technique in developing layups with tailored, variable stiffness morphology. The steered patterns of fiber tows with and without overlaps produce residual deformations that are distinctive from traditional layups. Digital image correlation was used to measure the AFP lamina coefficients of thermal expansion, which were incorporated into finite element analyses (FEA) to model the cooling phase of the cure cycle. The effects of nonlinear analysis and temperature-dependent lamina properties calculated using self-consistent field micromechanics, on the resulting residual deformation of shells, were also modeled. The predicted residual deformation was analyzed by considering out-of-roundness in cylindrical shells and compared to the experimental results. The shell FEA results were well-correlated with the overall deformed shape of the AFP cylinder with overlaps, while the shell FEA model of the AFP cylinder without overlaps did not show as good of qualitative match of the deformation pattern. Analytical correlation with measured results were insensitive to material softening at elevated temperatures, geometric nonlinearities, and variations in measured lamina thermal properties. To improve the accuracy of the residual deformation analysis, these results suggest that the thermo-chemical shrinkages preceding the cooldown should be considered, as well as possible variations in ply level microstructure due to the presence of the embedded fiber tow gaps and overlaps.

Composites↗
NASA NTRS2008

Structure Computation of Quiet Spike[Trademark] Flight-Test Data During Envelope Expansion

System identification or mathematical modeling is used in the aerospace community for development of simulation models for robust control law design. These models are often described as linear time-invariant processes. Nevertheless, it is well known that the underlying process is often nonlinear. The reason for using a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades, the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B Quiet Spike(TradeMark) aeroservoelastic flight-test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description that may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance for the development of robust parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion, which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B Quiet Spike aeroservoelastic flight-test data for several flight conditions that 1) linear models are inefficient for modeling aeroservoelastic data, 2) nonlinear identification provides a parsimonious model description while providing a high percent fit for cross-validated data, and 3) the model structure and parameters vary as the flight condition is altered.

Kukreja, Sunil L.↗
NASA NTRS1982

Nonlinear Marangoni convection in bounded layers. I - Circular cylindrical containers. II - Rectangular cylindrical containers

Liquid undergoing nonlinear Marangoni instability in a circular cylinder is examined, with attention given to roll-cell development and interaction. Surface deflections are neglected and the side walls are considered as adiabatic and impenetrable, allowing the liquid to freely slip. The nonlinear convective states are calculated and their stability is defined. The behavior and amplitude of cells forming in the liquid, heated from below, are modeled in order to derive all the transport properties. A new small parameter is formulated which is related to the critical Marangoni number of the infinite matrix expressing the eigenvalue expansion of the problem. The observed roll cell amplitudes and transport properties are shown to be available from simple eigenvalues, with double eigenvalues, indicating the existence of two roll-states as predicted by linear theory, nonlinear theory indicates transitions from one steady convective state to another.

Rosenblat, S.↗
DOE OSTI2020

Lifetime renormalization of driven weakly anharmonic superconducting qubits. II. The readout problem

Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number-nonconserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. Here, we present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e., Kerr interactions) shows that number-nonconserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly nonlinear degrees of freedom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1977

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

Kim, H.↗
NASA NTRS1979

Nonlinear effects on sound propagation through high subsonic Mach number flows in variable area ducts

A nonlinear theory for sound propagation in variable area ducts carrying a nearly sonic flow is presented. Linear acoustic theory is shown to be singular and the detailed nature of the singularity is used to develop the correct nonlinear theory. The theory is based on a quasi-one dimensional model. It is derived by the method of matched asymptotic expansions. In a nearly chocked flow, the theory indicates the following processes to be acting: a transonic trapping of upstream propagating sound causing an intensification of this sound in the throat region of the duct; generation of superharmonics and an acoustic streaming effect; development of shocks in the acoustic quantities near the throat. Several specific problems are solved analytically and numerical parameter studies are carried out. Results indicate that appreciable acoustic power is shifted to higher harmonics as shocked conditions are approached. The effect of the throat Mach number on the attenuation of upstream propagating sound excited by a fixed source is also determined.

Callegari, A. J.↗
NASA NTRS1990

Self-similar evolution of the nonlinear magnetic buoyancy instability

A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.

Shibata, K.↗
NASA NTRS1998

Some Comments on the Status of Shell Theory at the End of the 20th Century: Complaints and Correctives

This review is divided into complaints and correctives. Complaints are directed at: sloppy refereeing and editing; authors who fail to read or acknowledge what others have done; the mis-naming or mis-crediting of results; the misunderstanding and misuse of the Kirchhoff hypothesis; inflated claims of accuracy based on overly-simplified benchmark problems; the failure to appreciate the inherent errors in various shell models; the failure to appreciate that the physical response and mathematical structure of shell theory are fundamentally different from 3-dimensional elasticity; and the irrelevance of Cosserat-type theories. Correctives include a simple, straight-forward derivation of a general nonlinear dynamic shell theory with the following features: (1) the equations of motion and kinematics (and those of thermodynamics, if desired) are exact consequences of their 3-dimensional counterparts; (2) there are no asymptotic or series expansions through the thickness; (3) all approximations (including the Kirchhoff Hypothesis) occur in the constitutive relations; (4) in static problems, there is a mixed form of the governing equations involving a mixed-energy density and exhibiting remnants of the well-known static-geometric duality of linear theory which is numerically robust because the limiting cases of nonlinear membrane theory and inextensional bending theory fall out naturally. (These latter two special cases are known to produce numerical nightmares unless treated with great care); and (5) all equations may be expressed in coordinate-free form (although, sometimes, a hybrid form is shown to be superior).

Simmonds, James G.↗
DOE OSTI2024

Development of Modified Perturbation Solutions to the One-Phase Stefan Problems With a Convective Boundary

The classical Stefan problem is used to track the moving solid-liquid interface during the freezing process. Perturbation theory has often been applied to find an approximate analytical solution due to the nonlinearity of the moving interface. However, the Stefan number (i.e., the sensible over latent heat) must be small and usually less than 0.01 to assume the perturbation expansion, which in turn limits the thermal engineering applications. In this study, a modified perturbation solution is developed by adding a correction term after the leading-order solution to be valid for a much wider range of Stefan numbers (i.e., 0.01 less than or equal to Ste less than or equal to 1). Specifically, a one-phase Stefan problem is first formulated subjected to a convective boundary in the Cartesian, cylindrical, and spherical coordinate systems for inward solidification. The leading-order solution is calculated based on the regular perturbation theory, while the correction term is obtained using the Monte-Carlo method and a multi-variant regression. Results show that the correction term has a linear relationship with the Stefan number and is not significantly influenced by the Biot number. The proposed modified perturbation solution can accurately and rapidly predict the nonlinear moving interface motion for the freezing process.

DIRECT ENERGY CONVERSION,MATHEMATICS AND COMPUTING↗
NASA NTRS1983

An overview of two nonlinear supersonic wing design studies

The progress of two studies which apply nonlinear aerodynamics to supersonic wing design is reviewed. The first study employed a nonlinear potential flow code to design wings for high lift and low drag due to lift by employing a controlled leading-edge expansion in which the crossflow accelerates to supercritical conditions and decelerates through a weak shock. The second study utilized a modified linearized theory code to explore the concept of using 'attainable' leading-edge thrust as a guide for selecting a wing leading-edge shape (planform and radius) for maintaining attached flow and maximizing leading-edge thrust. Experimental and theoretical results obtained during the course of these two studies are discussed.

Miller, D. S.↗
NASA NTRS1985

Cell wall elasticity: I. A critique of the bulk elastic modulus approach and an analysis using polymer elastic principles

The traditional bulk elastic modulus approach to plant cell pressure-volume relations is inconsistent with its definition. The relationship between the bulk modulus and Young's modulus that forms the basis of their usual application to cell pressure-volume properties is demonstrated to be physically meaningless. The bulk modulus describes stress/strain relations of solid, homogeneous bodies undergoing small deformations, whereas the plant cell is best described as a thin-shelled, fluid-filled structure with a polymer base. Because cell walls possess a polymer structure, an alternative method of mechanical analysis is presented using polymer elasticity principles. This initial study presents the groundwork of polymer mechanics as would be applied to cell walls and discusses how the matrix and microfibrillar network induce nonlinear stress/strain relationships in the cell wall in response to turgor pressure. In subsequent studies, these concepts will be expanded to include anisotropic expansion as regulated by the microfibrillar network.

Plants/chemistry/cytology/ultrastructure↗
DOE OSTI2021

The Role of Water and Hydroxyl Groups in the Structures of Stetindite and Coffinite, MSiO 4 (M = Ce, U)

Orthosilicates adopt the zircon structure types ( I 4 1 /amd ), consisting of isolated SiO 4 tetrahedra joined by A-site metal cations, such as Ce and U. They are of significant interest in the fields of geochemistry, mineralogy, nuclear waste form development, and material science. Stetindite (CeSiO 4 ) and coffinite (USiO 4 ) can be formed under hydrothermal conditions despite both being thermodynamically metastable. Water has been hypothesized to play a significant role in stabilizing and forming these orthosilicate phases, though little experimental evidence exists. To understand the effects of hydration or hydroxylation on these orthosilicates, in situ high-temperature synchrotron and laboratory-based X-ray diffraction was conducted from 25 to ~850 °C. Stetindite maintains its I 4 1 /amd symmetry with increasing temperature but exhibits a discontinuous expansion along the a- axis during heating, presumably due to the removal of water confined in the [001] channels, which shrink against thermal expansion along the a -axis. Furthermore, additional in situ high-temperature Raman and Fourier transform infrared spectroscopy also confirmed the presence of the confined water. Coffinite was also found to expand nonlinearly up to 600 °C and then thermally decompose into a mixture of UO 2 and SiO 2 . A combination of dehydration and dehydroxylation is proposed for explaining the thermal behavior of coffinite synthesized hydrothermally. Additionally, we investigated high-temperature structures of two coffinite-thorite solid solutions, uranothorite (U x Th 1– x SiO 4 ), which displayed complex variations in composition during heating that was attributed to the negative enthalpy of mixing. Lastly, for the first time, the coefficients of thermal expansion of CeSiO 4 , USiO 4 , U 0.46 Th 0.54 SiO 4 , and U 0.9 Th 0.1 SiO 4 were determined to be α V = 14.49 × 10 –6 , 14.29 × 10 –6 , 17.21 × 10 –6 , and 17.23 × 10 –6 °C –1 , respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
NASA NTRS1972

Nonlinear instability of a helicopter blade.

The nonlinear equations of flap-lag coupled with oscillation of a torsionally rigid blade are derived. The solution is established by a simplified asymptotic expansion procedure of multiple time scales. The region of stability and limit cycle oscillation and its comparison with numerical results are presented.

Tong, P.↗
NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗