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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.

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At least 235 records · Page 13

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NASA NTRS1981

A multiloop generalization of the circle criterion for stability margin analysis

In order to provide a theoretical tool well suited for use in characterizing the stability margins (e.g., gain and phase margins) of multiloop feedback systems, multiloop input-output stability results generalizing the circle stability criterion are considered. Generalized conic sectors with 'centers' and 'radii' determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency-dependent convex set of modeling errors (including nonlinearities, gain variations, and phase variations) which the system must be able to tolerate in each feedback loop without instability. The resulting stability criterion gives sufficient conditions for closed-loop stability in the presence of such frequency-dependent modeling errors, even when the modeling errors occur simultaneously in all loops.

Safonov, M. G.↗

NASA NTRS2011

Assessment of MODIS Thermal Emissive Band On-Orbit Calibration

Sixteen Moderate Resolution Imaging Spectroradiometer thermal emissive bands (TEBs) cover the wavelength from 3.75 to 14.24 m. TEB calibration uses data collected from the detector responses to the onboard blackbody (BB) and space view. The BB was designed to operate either at a constant temperature for detector linear gain calibration or at temperatures varying from ambient ( 270 K) to 315 K for on-orbit characterization of nonlinear coefficients. In this paper, we assess TEB on-orbit calibration performance in two aspects: One is to review the calibration trending on the orbital, daily, and multiyear timescales, and the other is to analyze the on-orbit calibration radiance uncertainty and its impact on the calibration. The calibration trending confirms the detector response dependence on the instrument temperature. The temperature trending and prelaunch characterization provide the basis for determining the calibration radiance source temperature range and uncertainties. An analytical approach was used to assess the impacts of onboard radiance uncertainties. The BB emission uncertainty, resulting from the temperature measurement error and emissivity uncertainty, causes a calibration uncertainty up to 0.3%, a value decreasing with the band wavelength. The BB nonblackness effect is analyzed and found to be insignificant. For the band with the lowest BB emissivity, the nonblackness affects the calibration radiance by less than 0.08%. The cavity emission uncertainty and the scan-mirror emission uncertainty both cause a less than 0.1% calibration uncertainty. The analysis of the nonlinear calibration coefficient uncertainty shows that its effect on the low Earth-view brightness-temperature range varies by band and is generally insignificant.

Chang, Tiejun↗

DOE OSTI2023

Semidefinite programming algorithm for the quantum mechanical bootstrap

Here, we present a semidefinite programming algorithm to find eigenvalues of Schrödinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasibility problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable that measures the failure of positivity. To illustrate the method we are able to obtain high-precision, sharp bounds on eigenenergies for arbitrary confining polynomial potentials in one dimension.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Guided Mode Evolution and Ionization Injection in Meter-Scale Multi-GeV Laser Wakefield Accelerators

Here, we show that multi-GeV laser wakefield electron accelerators in meter-scale, low density hydrodynamic plasma waveguides operate in a new nonlinear propagation regime dominated by sustained beating of lowest order modes of the ponderomotively modified channel; this occurs whether or not the injected pulse is linearly matched to the guide. For a continuously doped gas jet, this emergent mode beating effect leads to axially modulated enhancement of ionization injection and a multi-GeV energy spectrum of multiple quasimonoenergetic peaks; the same process in a locally doped jet produces single multi-GeV peaks with <10% energy spread. A three-stage model of drive laser pulse evolution and ionization injection characterizes the beating effect and explains our experimental results.

43 PARTICLE ACCELERATORS↗

NASA NTRS1977

Generalized computer-aided discrete time domain modeling and analysis of dc-dc converters

A generalized discrete time domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller, and operating in both continuous and discontinuous inductor current. State space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact and easy to use.

Lee, F. C.↗

NASA NTRS1979

SPAR thermal analysis processors reference manual, system level 16. Volume 1: Program executive. Volume 2: Theory. Volume 3: Demonstration problems. Volume 4: Experimental thermal element capability. Volume 5: Programmer reference

User instructions are given for performing linear and nonlinear steady state and transient thermal analyses with SPAR thermal analysis processors TGEO, SSTA, and TRTA. It is assumed that the user is familiar with basic SPAR operations and basic heat transfer theory.

Marlowe, M. B.↗

NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗

DOE OSTI2025

Benchmark of numerical modeling approaches on the systematic performance evaluation of wave energy converters

Different numerical modeling methods have been developed and applied to evaluate a variety of performance indicators of wave energy converters (WECs), including the power performance, structural loads, levelized cost of energy, etc. Based on the modeling fidelity, the commonly used numerical modeling approaches can be classified as linear modeling, weakly nonlinear modeling and fully nonlinear modeling approaches. Each method differs in accuracy and computational efficiency, making them suitable for different stages of WEC design. However, the selection of modeling approach could significantly impact evaluation outcomes. For instance, simplified linear models may underestimate structural loads or overestimate energy production in some operational conditions, potentially leading to less cost-effective designs. Given the widespread utilization of these models, it is essential to understand the uncertainties brought by them in performance evaluations. This work is dedicated to benchmarking different linear-potential-flow-based numerical models for evaluating the systematic performance of WECs. Three representative numerical modeling approaches are considered in this work, including linear frequency-domain modeling, statistically linearized spectral-domain modeling and Cummins equation-based nonlinear time-domain modeling. A generic point absorber WEC is considered as the research reference in this work, and different sea sites are taken into account. The numerical models are utilized to predict critical performance indicators, including power performance, the annual energy production, the capacity factor, the levelized cost of energy and the PTO fatigue loads. By comparing the results, this work identifies the uncertainties associated with different modeling approaches in evaluating WEC performance.

Fatigue↗

DOE OSTI2024

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Conditional VAEs↗

NASA NTRS1996

Variations on the Davenport Gyroscope Calibration Algorithm

This paper presents a number of variations on the Davenport algorithm for in-flight gyroscope recalibration, or first order initial calibration, specifically tailored for use with a minimum of satellite telemetry data. Central to one of the techniques described is the use of onboard integration of gyroscope data together with a detailed model of scheduled satellite slew profiles. Methods are presented for determining adjustments to either parameters for the standard linear model (i.e., a drift rate bias vector and/or a scale factor/alignment transformation matrix) or individual gyroscope scale parameters, both linear and nonlinear, in cases where the alignments are well known. The results of applying the methods in an analysis of the temporal evolution and nonlinear response of the gyroscopes installed on the Hubble Space Telescope following its first servicing mission are discussed. The two effects, when working coherently, have been found to result in slew errors of almost 1 arcsecond per degree. Procedures for selecting optimal operational gyroscope parameters subject to the constraint of using a linear model are discussed.

Welter, G.↗

NASA NTRS1989

Automatic control of cryogenic wind tunnels

Inadequate Reynolds number similarity in testing of scaled models affects the quality of aerodynamic data from wind tunnels. This is due to scale effects of boundary-layer shock wave interaction which is likely to be severe at transonic speeds. The idea of operation of wind tunnels using test gas cooled to cryogenic temperatures has yielded a quantrum jump in the ability to realize full scale Reynolds number flow similarity in small transonic tunnels. In such tunnels, the basic flow control problem consists of obtaining and maintaining the desired test section flow parameters. Mach number, Reynolds number, and dynamic pressure are the three flow parameters that are usually required to be kept constant during the period of model aerodynamic data acquisition. The series of activity involved in modeling, control law development, mechanization of the control laws on a microcomputer, and the performance of a globally stable automatic control system for the 0.3-m Transonic Cryogenic Tunnel (TCT) are discussed. A lumped multi-variable nonlinear dynamic model of the cryogenic tunnel, generation of a set of linear control laws for small perturbation, and nonlinear control strategy for large set point changes including tunnel trajectory control are described. The details of mechanization of the control laws on a 16 bit microcomputer system, the software features, operator interface, the display and safety are discussed. The controller is shown to provide globally stable and reliable temperature control to + or - 0.2 K, pressure to + or - 0.07 psi and Mach number to + or - 0.002 of the set point value. This performance is obtained both during large set point commands as for a tunnel cooldown, and during aerodynamic data acquisition with intrusive activity like geometrical changes in the test section such as angle of attack changes, drag rake movements, wall adaptation and sidewall boundary-layer removal. Feasibility of the use of an automatic Reynolds number control mode with fixed Mach number control is demonstrated.

Balakrishna, S.↗

NASA NTRS1972

The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets

An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering.

Lores, M. E.↗

NASA NTRS1994

Acoustic instability driven by cosmic-ray streaming

We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.

Begelman, Mitchell C.↗

DOE OSTI2023

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Farfield viscous effects in nonlinear noise propagation

Discussion of the method of parametric differentiation in application to predictions of farfield noise propagation in both lossless and dissipative media. It is shown that, in the lossless medium, the governing equation, transformed to parameter space, reduces to a wave equation in the farfield. In the dissipative medium, the system of nonlinear partial differential equations, transformed to parameter space, reduces to a linear partial differential equation of the propagating type which contains a third-order derivative as well as the wave operator.

Harris, W. L., Sr.↗

NASA NTRS1975

A fast semidirect method for computing transonic aerodynamic flows

A fast, semidirect, iterative computational method, previously introduced for finite-difference solution of subsonic and slightly supercritical flow over airfoils, is extended both to apply to strongly supercritical conditions and to include full second-order accuracy in computing inviscid flows over airfoils. The nonlinear small-disturbance equations are solved iteratively by a direct, linear, elliptic solver. General, fully conservative, type-dependent difference equations are formulated, including parabolic- and shock-point transition operators that provide consistency with the integral conservation laws. These equations specialize to either first-order or to fully second-order-accurate equations. Various free parameters are evaluated for rapid convergence of the first-order scheme. Resulting pressure distributions and computing times are compared with the improved Murman-Cole line-relaxation method.

Martin, E. D.↗

NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗

NASA NTRS1985

Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates

The Harten (1983, 1984) total variation-diminishing (TVD) schemes, constituting a one-parameter explicit and implicit, second-order-accurate family, have the property of not generating spurious oscillations when applied to one-dimensional, nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. These methods are presently extended to the multidimensional hyperbolic conservation laws in curvilinear coordinates. Means by which to linearize the implicit operator and solution strategies, in order to improve the computation efficiency of the implicit algorithm, are discussed. Numerical experiments with steady state airfoil calculations indicate that the proposed linearized implicit TVD schemes are accurate and robust.

Yee, H. C.↗