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Results for “Analytic derivatives”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Experimental and Numerical Optimization of a High-Lift System to Improve Low-Speed Performance, Stability, and Control of an Arrow-Wing Supersonic Transport

An investigation was performed to evaluate leading-and trailing-edge flap deflections for optimal aerodynamic performance of a High-Speed Civil Transport concept during takeoff and approach-to-landing conditions. The configuration used for this study was designed by the Douglas Aircraft Company during the 1970's. A 0.1-scale model of this configuration was tested in the Langley 30- by 60-Foot Tunnel with both the original leading-edge flap system and a new leading-edge flap system, which was designed with modem computational flow analysis and optimization tools. Leading-and trailing-edge flap deflections were generated for the original and modified leading-edge flap systems with the computational flow analysis and optimization tools. Although wind tunnel data indicated improvements in aerodynamic performance for the analytically derived flap deflections for both leading-edge flap systems, perturbations of the analytically derived leading-edge flap deflections yielded significant additional improvements in aerodynamic performance. In addition to the aerodynamic performance optimization testing, stability and control data were also obtained. An evaluation of the crosswind landing capability of the aircraft configuration revealed that insufficient lateral control existed as a result of high levels of lateral stability. Deflection of the leading-and trailing-edge flaps improved the crosswind landing capability of the vehicle considerably; however, additional improvements are required.

Hahne, David E.↗
DOE OSTI2020

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗
NASA NTRS1972

A multiple-impulse function for orbital transfer and its derivatives

A multiple-impulse function is represented as a sequence of single-impulse functions. The single-impulse transfer which yields the velocity change required to transfer from a specified initial orbit to a partially specified final orbit is developed. Analytic derivatives of the function are obtained for use in optimization techniques. A four-impulse transfer is outlined. The analytic derivatives may allow more efficient optimization than numerical derivatives do.

Kibler, J. F.↗
NASA NTRS1978

Efficiency of unconstrained minimization techniques in nonlinear analysis

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Kamat, M. P.↗
DOE OSTI2023

Analytical Large-Signal Modeling of Inverter-Based Microgrids With Koopman Operator Theory for Autonomous Control

The microgrid (MG) plays a crucial role in the energy transition, but its nonlinearity presents a significant challenge for large-signal power systems studies in the electromagnetic transient (EMT) time scale. In this paper, we develop a large-signal linear MG model that considers the detailed dynamics of the primary and zero-control levels based on the Koopman operator (KO) theory. Firstly, a set of observable functions is carefully designed to capture the nonlinear dynamics of the MG. The corresponding linear KO is then analytically derived based on these observables, resulting in the linear representation of the original nonlinear MG with observables as the new coordinate. The influence of external input on the system dynamics is also considered during the derivation, enabling control of the MG. We solve the voltage control problem using the traditional linear quadratic integrator (LQI) method to demonstrate that textbook linear control techniques can accurately control the original nonlinear MG via the developed KO-linearized MG model. Our proposed KO linearization method is generic and can be easily extended for different control objectives and MG structures using our analytical derivation procedure. Here, we validate the effectiveness of our methodology through various case studies.

25 ENERGY STORAGE↗
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
DOE OSTI2022

Dual-map framework for noise characterization of quantum computers

In order to understand the capabilities and limitations of quantum computers, it is necessary to develop methods that efficiently characterize and benchmark error channels present on these devices. In this paper, we present a method that faithfully reconstructs a marginal (local) approximation of the effective noise (MATEN) channel, that acts as a single layer at the end of the circuit. We first introduce a dual-map framework that allows us to analytically derive expectation values of observables with respect to noisy circuits. These findings are supported by numerical simulations of the quantum approximate optimization algorithm (QAOA) that also justify the MATEN, even in the presence of nonlocal errors that occur during a circuit. Finally, we demonstrate the performance of the method on Rigetti's Aspen-11 quantum computer for QAOA circuits up to six qubits, successfully predicting the observed measurements on a majority of the qubits.

Sud, James↗
NASA NTRS1977

The design of hydraulic pressure regulators that are stable without the use of sensing line restrictors or frictional dampers

Parameters controlled in design determine the stability of hydraulic pressure regulators in service. The non-linear sensing line restrictor can provide stability, but degrades the transient response. Linear damping is not always physically realizable and is sensitive to clearance and viscosity. Design relationships are analytically derived through which regulators can be made to be stable without the use of either of these damping means. The analytical distinctions between the parameters derived and those in prior literature are discussed. An analytically derived circuit component that stabilizes an otherwise unstable regulator and its experimental verification is described.

Gold, H.↗
DOE OSTI2023

Continental Scale Hydrostratigraphy: Comparing Geologically Informed Data Products to Analytical Solutions

Abstract This study synthesizes two different methods for estimating hydraulic conductivity (K) at large scales. We derive analytical approaches that estimate K and apply them to the contiguous United States. We then compare these analytical approaches to three‐dimensional, national gridded K data products and three transmissivity (T) data products developed from publicly available sources. We evaluate these data products using multiple approaches: comparing their statistics qualitatively and quantitatively and with hydrologic model simulations. Some of these datasets were used as inputs for an integrated hydrologic model of the Upper Colorado River Basin and the comparison of the results with observations was used to further evaluate the K data products. Simulated average daily streamflow was compared to daily flow data from 10 USGS stream gages in the domain, and annually averaged simulated groundwater depths are compared to observations from nearly 2000 monitoring wells. We find streamflow predictions from analytically informed simulations to be similar in relative bias and Spearman's rho to the geologically informed simulations. R ‐squared values for groundwater depth predictions are close between the best performing analytically and geologically informed simulations at 0.68 and 0.70 respectively, with RMSE values under 10 m. We also show that the analytical approach derived by this study produces estimates of K that are similar in spatial distribution, standard deviation, mean value, and modeling performance to geologically‐informed estimates. The results of this work are used to inform a follow‐on study that tests additional data‐driven approaches in multiple basins within the contiguous United States.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Valence-band hybridization in sulphides

The hybridization state in solids often defines the critical chemical and physical properties of a compound. However, it is difficult to spectroscopically detect and evaluate hybridization beyond just general fingerprint signatures. Here, the valence-band hybridization of metal d-derived bands (short: “metal d bands”) in selected metal sulphides is studied with a combined spectroscopic and theoretical approach to derive deeper insights into the fundamental nature of such compounds. The valence bands of the studied sulphides are comprised of hybrid bands derived from the metal d, S 3s, and S 3p states. Employing S K and L 2,3 X-ray emission spectroscopy and spectra calculations based on density functional theory, the degree of hybridization (i.e., the covalency) of these bands can be directly probed as a function of their relative energies. We find that the relative intensity of the “metal d band” features in the spectra scales with the inverse square of the energy separation to the respective sulfur-derived bands, which can be analytically derived from a simple two-orbital model. This study demonstrates that soft X-ray emission spectroscopy is a powerful tool to study valence state hybridization, in particular in combination with hard X-ray emission spectroscopy, promising a broad impact in many research fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

Rate Constant for the Reaction CH3 + CH3 Yields C2H6 at T = 155 K and Model Calculation of the CH3 Abundance in the Atmospheres of Saturn and Neptune

The column abundances of CH3 observed by the Infrared Space Observatory (ISO) satellite on Saturn and Neptune were lower than predicted by atmospheric photochemical models, especially for Saturn. It has been suggested that the models underestimated the loss of CH3 due to poor knowledge of the rate constant k of the CH3 + CH3 self-reaction at the low temperatures and pressures of these atmospheres. Motivated by this suggestion, we undertook a combined experimental and photochemical modeling study of the CH3 + CH3 reaction and its role in determining planetary CH3 abundances. In a discharge flow-mass spectrometer system, k was measured at T = 155 K and three pressures of He. The results in units of cu cm/molecule/s are k(0.6 Torr) = 6.82 x 10(exp -11), k(1.0 Torr) = 6.98 x 10(exp -11), and k(1.5 Torr) = 6.91 x 10(exp -11). Analytical expressions for k were derived that (1) are consistent with the present laboratory data at T = 155 K, our previous data at T = 202 K and 298 K, and those of other studies in He at T = 296-298 K and (2) have some theoretical basis to provide justification for extrapolation. The derived analytical expressions were then used in atmospheric photochemical models for both Saturn and Neptune. These model results reduced the disparity with observations of Saturn, but not with observations of Neptune. However, the disparity for Neptune is much smaller. The solution to the remaining excess CH3 prediction in the models relative to the ISO observations lies, to a large extent, elsewhere in the CH3 photochemistry or transport, not in the CH3 + CH3 rate.

Cody, Regina J.↗
DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

An alternative formulation of the global sensitivity equations

To optimize the performance of any system, the sensitivity derivatives of the system's output variables with respect to its input variables must be readily available. It is also desirable that these derivatives be inexpensive to calculate as the optimization process requires many evaluations of the output variables and their derivatives. Optimization methods that have been developed for use in automated structural design programs may not be extended for use in integrated multidisciplinary design programs until adequate means of calculating accurate sensitivity derivatives of complex, internally coupled systems have been developed. Until the development of the Global Sensitivity Equations (GSE), the only method of determining the sensitivity derivatives of coupled systems has been by using finite differences. Analytical or semi-analytical derivatives do not exist as there is no analytical solution to the coupled problem. Also, difficulties arise because the finite difference method is expensive as the system has to iterate to a converged solution for each incremental input variable. The method may not be accurate, and the choice of the input variable increment may cause the difference in the output variable to be insignificant compared to computer numerical error if the choice is too small, or the process may not predict the true value of the output variable if the increment is too large. The GSE allow the system's sensitivity derivatives to be calculated as functions of the component subsystem's (local) sensitivity derivatives. These local sensitivity derivatives are calculated from specifically decoupled subsystems, whereas the GSE account for total system coupling. Since the subsystems are decoupled, it may be possible for the local derivatives to be calculated by analytical or semi-analytical methods, which generally reduce cost and improve accuracy. Several academic problems have been solved using GSE and have demonstrated encouraging results.

James, Benjamin B.↗
NASA NTRSDate not supplied

AAM NC ATI TechTalk - Aerograph Architecture v1

Aerograph is NASA’s data management system for Advanced Air Mobility. Its mission is to support AAM research by providing a reliable and secure system that collects, stores, protects, and shares AAM data. Its vision is to provide a system that AAM research scientists, aerospace engineers, data scientists, and analysts trust for obtaining NC data and performing key analyses. The types of data Aerograph manages involves data related to flight test events, including: Aircraft Performance and Characterization (e.g., position reports) Airspace (e.g., operation intent, waypoints, and constraints) Environment (e.g., surface and wind weather) Infrastructure (e.g., surveillance coverage) Derivative Analytical Artifacts (e.g., glide path performance chart, 3D position chart, Integrated Data Product)

Aerograph↗
NASA NTRS1972

Pre-emphasis determination for an S-band constant bandwidth FM/FM station

Pre-emphasis schedules are given for 11 constant-bandwidth FM subcarriers modulating an S band transmitter at three receiver signal to noise ratios (i.e., 9, 15, and 25 dB). The criterion for establishing these pre-emphasis curves is the achievement, at various receiver intermediate frequency signal to noise ratios, of equal receiver output signal to noise ratios for all channels. It is realized that these curves may not be the optimum pre-emphasis curves based on overall efficiency or maximum utilization of the allotted spectrum, but they are near-optimum for data with channels which require equal output signal to noise ratios, such as spectral densities. The empirically derived results are compared with a simplified, analytically derived schedule and the primary differences are explained. The S band pre-emphasis schedule differs from the lower frequency VHF case. Since most proportional bandwidth and constant bandwidth systems use ground based recorders and some use flight recorders (as the Saturn systems did on VHF proportional bandwidth telemetry), the effects of these recorders are discussed and a modified pre-emphasis schedule is presented showing the results of this study phase.

Wallace, G. R.↗
NASA NTRS1973

Preemphasis for an S-band constant bandwidth FM/FM system.

Preemphasis schedules are given for 11 constant-bandwidth FM subcarriers modulating an S-band transmitter at various receiver SNRs (9 dB, 15 dB and 25 dB). The criterion for establishing these preemphasis curves is the achievement, at various receiver IF SNR, of equal receiver output SNR for all channels. The empirically derived results are compared with a simplified, analytically derived schedule and the primary differences are explained. The S-band preemphasis schedule is also found to differ from the lower frequency VHF case.

Wallace, G. R.↗