Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear expansion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nonlinear diffusion in the solid phase

A Fourier series expansion method has been used to develop simple and relatively accurate solutions for nonlinear Fickian diffusion in the solid phase. For the fundamental harmonic, the first term in the Fourier expansion is qualitatively similar but quantitatively quite different from the conventional exponential function. In contrast, the Fourier coefficients of the higher order harmonics are combinations of fast-decay and slow-decay components. The simple analytical results agree well with numerical solutions for one sample calculation.

Tsang, Tung↗
NASA NTRS1974

Finite-amplitude waves in cylindrical lined ducts

A second-order uniformly valid expansion is obtained for nonlinear waves propagating in a cylindrical duct lined with a point-reacting acoustic material that consists of a porous sheet followed by honey-comb cavities and backed by the impervious walls of the duct. The effect of the liner is taken into account by coupling the waves in the duct with those in the liner. As in the two-dimensional case, the nonlinearity increases the attenuation rate at all frequencies except in narrow bandwidths around the resonant frequencies, irrespective of the geometrical dimensions of the liner or the acoustic properties of the porous sheet.

Nayfeh, A. H.↗
NASA NTRS1974

Finite amplitude waves in two-dimensional lined ducts

A second-order uniform expansion is obtained for nonlinear wave propagation in a two-dimensional duct lined with a point-reacting acoustic material consisting of a porous sheet followed by honeycomb cavities and backed by the impervious wall of the duct. The waves in the duct are coupled with those in the porous sheet and the cavities. An analytical expression is obtained for the absorption coefficient in terms of the sound frequency, the physical properties of the porous sheet, and the geometrical parameters of the flow configuration. The results show that the nonlinearity flattens and broadens the absorption vs. frequency curve, irrespective of the geometrical dimensions or the porous material acoustic properties, in agreement with experimental observations.

Nayfeh, A. H.↗
NASA NTRS1993

The nature of the hydrogen tori of Titan and Triton

The nature of the hydrogen tori of Titan and Triton is examined. Critical time scales of the two tori are discussed. For the Titan torus, where atom-atom collisions are not important, the time scale for solar radiation pressure to act on the system is shown to be comparable to the hydrogen lifetime due to ionization and charge exchange losses by solar, magnetospheric, and solar wind processes. The solar radiation pressure then provides a mechanism which destroys the initial azimuthal symmetry of the hydrogen atom orbits about the planet and causes atom orbits to move inward and to collide with the planet on its dusk side. For Triton, the atom-atom collision time scale dominates all other time scales in the system. The evolution of the torus is then an inherently nonlinear problem that depends upon the collisional redistribution of atom-orbit velocities in the presence of a planetary gravitational force field. This nonlinear process introduces an expansion mechanism into the torus problem which dramatically alters its structure.

Smyth, William H.↗
NASA NTRS1999

Wind Speed Measurement from Bistatically Scattered GPS Signals

Instrumentation and retrieval algorithms are described which use the forward, or bistatically scattered range-coded signals from the Global Positioning System (GPS) radio navigation system for the measurement of sea surface roughness. This roughness is known to be related directly to the surface wind speed. Experiments were conducted from aircraft along the TOPEX ground track, and over experimental surface truth buoys. These flights used a receiver capable of recording the cross correlation power in the reflected signal. The shape of this power distribution was then compared against analytical models derived from geometric optics. Two techniques for matching these functions were studied. The first recognized the most significant information content in the reflected signal is contained in the trailing edge slope of the waveform. The second attempted to match the complete shape of the waveform by approximating it as a series expansion and obtaining the nonlinear least squares estimate. Discussion is also presented on anomalies in the receiver operation and their identification and correction.

Garrison, James L.↗
DOE OSTI2025

A DATA EFFICIENT SPARSE MODELING FRAMEWORK FOR POWER ESTIMATION IN WATER TREATMENT SENSING OPERATIONS

With increasing freshwater scarcity, advanced process design mechanisms such as Closed-Circuit Reverse Osmosis (CCRO) and Digital/Physical Twin systems are gaining traction in water treatment and reuse operations. While digital and physical twin models enable improved system insight and control, their development is often expensive and computationally intensive, requiring large volumes of synthetic or experimental data to characterize underlying process dynamics. This work introduces a sparse surrogate modeling framework to estimate power consumption from measured flow and pressure variables, along with their nonlinear polynomial and interaction expansions. To ensure model reliability and reduce overfitting, a two-stage pipeline is proposed. First, a dynamic data filtering algorithm is employed to remove uninformative observations and transient operational states. Second, a sparse penalized regression technique is applied to select a minimal set of parsimonious features. The proposed model achieves high sparsity, retaining only 7 out of 34 candidate features (≈79.41% sparsity) while delivering a root mean square error (RMSE) of 0.072 on the test dataset.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗
NASA NTRS1978

The effect of nonlinear diffusive heat transport in a simple climate model

The effects of nonlinear diffusive heat transport in North's (1975) model is reexamined. By inserting the nonlinearity into the original energy balance equation rather than the spectrally transformed linear algebraic equations, and including one more mode in the spectral expansion, it is found that nonlinear diffusion does give a significantly different sensitivity for states near the current climate. For linear diffusion, an increase of 0.1% of the solar constant from the present value is sufficient to melt all the ice on the earth, whereas an increase of about five times as large is required for nonlinear diffusion. This difference in sensitivity shows the importance of dynamical modeling in simple climate models.

Lin, C. A.↗
DOE OSTI2021

Online Monitoring System for Concrete Structures Affected by Alkali-Silica Reaction

This report presents a comprehensive study of developing ultrasonic wave and acoustic emission (AE) techniques for long-term monitoring of alkali-silica reaction (ASR) development in concrete. Small, medium, and full-scale concrete specimens were cast, conditioned, and monitored for various periods, from at least one year to 2.4 years. The reactive concrete specimens contain coarse or fine reactive aggregates to study the effects of different types of reactive aggregates. Confinements were also designed to simulate the 2-dimensional confinement effects of reinforcement in the shield building of nuclear power plants. The concrete specimens were stored in a environmental chamber with high humidity and high temperature to accelerate the ASR development. The ultrasonic monitoring data shows high sensitivity to ASR development and could detect cracking initiation well before visible surface cracks occurred. However, the linear ultrasonic analysis based on wave velocity is strongly affected by temperature variation. Therefore, a nonlinear ultrasonic method was proposed to measure thermally induced nonlinear acoustic responses of concrete (thermal modulation of ultrasonic wave). The measured nonlinear acoustic parameter shows a high correlation with ASR expansion across specimens with different reactive aggregates and confinement conditions. The same conclusion was obtained from nonlinear resonance tests on small concrete prisms. Compared to the linear acoustic methods, the nonlinear tests show high sensitivities to ASR damage from internal microcracking initiation at the early stage to visible cracks at the late stage of ASR. The attributes of the thermal modulation of nonlinear ultrasonic method include high sensitivity, immunity to temperature effects, and strong correlation with ASR expansion, which demonstrate great potentials of the nonlinear ultrasonic method for diagnosis of ASR damage and prediction of concrete deterioration process. Acoustic emission is a passive sensing technique for damage assessment, and access to only one surface is needed even for thick and heavily reinforced elements such as the walls utilized for nuclear shield building. Additionally, relatively few sensors are required to monitor the progression of the damage process. Results indicate that the AE data can be related to the damage rating index, which is a petrography-based means of assessing damage due to ASR in reinforced concrete. Furthermore, AE is capable of detecting ASR damage long before surface cracking is visually noticeable. Boundary conditions play in important role in the progression of ASR damage and differences in boundary conditions are reflected in the AE data. Entropy based data assessment methods provide a means to assess the damage state, and convolutional neural network based data assessment provided a means to assess the damage state in real-time. Results indicate that artificial neural network models may be used as a means to predict volumetric expansion based on AE data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗
NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗
NASA NTRS1990

Some theoretical aspects of boundary layer stability theory

Increased understanding in recent years of boundary layer transition has been made possible by the development of strongly nonlinear stability theories. After some twenty or so years when nonlinear stability theory was restricted to the application of the Stuart-Watson method (or less formal amplitude expansion procedures), there now exist strongly nonlinear theories which can describe processes which have an 0(1) effect on the basic state. These strongly nonlinear theories and their possible role in pushing theoretical understanding of transition ever further into the nonlinear regime are discussed.

Hall, Philip↗
DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗
DOE OSTI2024

Joint Expansion Planning of Power and Water Distribution Networks

This research considers the joint expansion planning of power and water distribution networks, which are interdependent at various levels. We consider the dependency arising through the power consumption of pumps and develop models for integrating new components into existing networks. Then, we formulate the joint expansion planning as a Mixed Integer Nonlinear Program (MINLP). Applying this MINLP to a small-scale test network, we illustrate the advantages offered by joint expansion planning, such as increased flexibility and reduced costs and redundancy, over independently expanding power and water distribution networks.

expansion planning↗
NASA NTRS1972

Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight

Equations for large coupled flap-lag motion of hingeless elastic helicopter blades are consistently derived. Only torsionally-rigid blades excited by quasi-steady aerodynamic loads are considered. The nonlinear equations of motion in the time and space variables are reduced to a system of coupled nonlinear ordinary differential equations with periodic coefficients, using Galerkin's method for the space variables. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The resulting system of nonlinear equations has been solved, using an asymptotic expansion procedure in multiple time scales. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing function, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified, and the basic physical mechanism of coupled flap-lag response becomes clear. The effect of forward flight is obtained with the requirement of trimmed flight at fixed values of the thrust coefficient.

Friedmann, P.↗
NASA NTRS1985

Large eddy interactions in a turbulent channel flow

The dynamic processes of large eddies in a turbulent channel flow have been examined by utilizing an orthogonal expansion of the velocity fluctuation, known in the literature as the Proper Orthogonal Decomposition Theorem. The mathematical form of these functions is unknown in contrast to the Fourier analysis. Attention is focused on the nonlinear, turbulence-turbulence interaction process in the dynamical equation for large eddies (the first term in the expansion). The nonlinear interactions of the components of the first mode are treated exactly, but influences of higher modes are modeled. This requires adjustment of both the skewness and the effective Reynolds number so that the energy equilibrium of the large eddies is ensured when the mean velocity distribution is assumed known for experiments. Computational results show that the first mode contributes significantly to turbulent intensities and possesses a structural and statistical character similar to that of the entire flow.

Hong, S. K.↗
NASA NTRS1989

Nonlinear Curve-Fitting Program

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Everhart, Joel L.↗
DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗