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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

On the energy dependence of the radial diffusion coefficient and spectra of inner radiation belt particles - Analytic solutions and comparison with numerical results

A theoretical method by which the energy dependence of the radial diffusion coefficient may be deduced from spectral observations of the particle population at the inner edge of the earth's radiation belts is presented. This region has previously been analyzed with numerical techniques; in this report an analytical treatment that illustrates characteristic limiting cases in the L shell range where the time scale of Coulomb losses is substantially shorter than that of radial diffusion (L approximately 1-2) is given. It is demonstrated both analytically and numerically that the particle spectra there are shaped by the energy dependence of the radial diffusion coefficient regardless of the spectral shapes of the particle populations diffusing inward from the outer radiation zone, so that from observed spectra the energy dependence of the diffusion coefficient can be determined. To insure realistic simulations, inner zone data obtained from experiments on the DIAL, AZUR, and ESRO 2 spacecraft have been used as boundary conditions. Excellent agreement between analytic and numerical results is reported.

Westphalen, H.↗
NASA NTRS1988

The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

Ng, C. F.↗
NASA NTRS1977

A singularity free analytical solution of artificial satellite motion with drag

The connection between the existing Delaunay-Similar and Poincare-Similar satellite theories in the true anomaly version is outlined for the J(2) perturbation and the new drag approach. An overall description of the concept of the approach is given while the necessary expansions and the procedure to arrive at the computer program for the canonical forces is delineated. The procedure for the analytical integration of these developed equations is described. In addition, some numerical results are given. The computer program for the algebraic multiplication of the Fourier series which creates the FORTRAN coding in an automatic manner is described and documented.

Scheifele, G.↗
NASA NTRS1982

Analytical solution for the drift behavior of Dynamics Explorer-B

The Dynamics Explorer (DE) mission was designed to explore the earth's magnetosphere, ionosphere, and plasmasphere. The DE mission employs two spacecraft, including DE-A and DE-B. The spacecraft were launched from the Western Test Range on Aug. 3, 1981, onboard the same Delta launch vehicle. The two spacecraft were placed in a coplanar polar orbit, with DE-A in a high altitude orbit (perigee = 570 km and apogee = 23174 km) and DE-B in a low altitude orbit (perigee = 309 km and apogee = 1013 km). In the present investigation, an attempt has been made to validate the flight data for DE-B with analytic and simulation results. The external torques acting on the spacecraft are represented in terms of tractable mathematical functions. A piecewise linear model of the superrotation of the upper atmosphere is assumed. The effect of individual torques on the long-term pitch axis motion is investigated using analytic and simulation methods. The results are found to be in very good agreement with the available flight data.

Sellappan, R. G.↗
DOE OSTI2023

Energy-Centric Cooperative Onramp Merging Strategy: An Analytical Solution

Cooperative highway onramp merging plays an important role in mitigating highway traffic congestion. A crucial component of a cooperative merging system is the merging sequence strategy, which determines each merging participant's order to reach the merging point. Existing merging sequence strategies can be classified into rule-based and optimization-based approaches. The rule-based strategies can be effortlessly implemented with a light online computational burden. However, they may not achieve the optimal energy efficiency. In contrast, the optimization-based strategies can yield the optimal merging sequence to minimize fuel consumption, but typically involve computationally expensive numerical optimization. To leverage the advantages from both sides, we propose a novel merging sequence strategy that can minimize fuel consumption while avoiding online numerical optimization. The key idea is to analytically formulate the expected fuel consumption of each merging participant. Using a realistic highway onramp scenario based on the NGSIM dataset, we validate the performance and the computational efficiency of the proposed merging sequence strategy via SUMO/SIMULINK joint simulation.

Wang, Zejiang↗
NASA NTRS2003

Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration

It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.

Koshak, William↗
DOE OSTI2021

Analytical solution for the cumulative wake of wind turbines in wind farms

This paper solves an approximate form of conservation of mass and momentum for a turbine in a wind farm array. The solution is a fairly simple explicit relationship that predicts the streamwise velocity distribution within a wind farm with an arbitrary layout. As this model is obtained by solving flow-governing equations directly for a turbine that is subject to upwind turbine wakes, no ad hoc superposition technique is needed to predict wind farm flows. A suite of large-eddy simulations (LES) of wind farm arrays is used to examine self-similarity as well as validity of the so-called conservation of momentum deficit for turbine wakes in wind farms. The simulations are performed with and without the presence of some specific turbines in the wind farm. This allows us to systematically study some of the assumptions made to develop the analytical model. A modified version of the conservation of momentum deficit is also proposed to provide slightly better results at short downwind distances, as well as in the far wake of turbines deep inside a wind farm. Model predictions are validated against the LES data for turbines in both full-wake and partial-wake conditions. While our results highlight the limitation in capturing the flow speed-up between adjacent turbine columns, the model is overall able to acceptably predict flow distributions for a moderately sized wind farm. Finally, the paper employs the new model to provide insights on the accuracy of common wake superposition methods.

17 WIND ENERGY↗
DOE OSTI2021

Hybrid Analytics Solution to Improve Coal Power Plant Operations

This project focused on developing advanced methods for thermal performance monitoring of a coal-fueled power plant. The specific goal was to develop and demonstrate a new thermal performance monitoring approach using a hybrid model that integrates a physics-based heat balance model with a machine learning-based pattern recognition model. The hybrid model enables increased accuracy and scope of the thermal analysis and an improved ability to monitor and detect changes in plant operation. This new approach takes full advantage of the individual model capabilities and creates an important new set of capabilities not previously possible using the two types of models separately. Using the heat balance model, a rich set of derived parameters (virtual sensors) are calculated from the measured plant operating data at each time point. The combined measured and derived data values are used by machine learning algorithms to create pattern recognition models over the range of normal unit operation. To create the monitoring models, historical data from normal operation of the plant is first processed by the heat balance model to compute the derived parameter data. The result is a greatly expanded set of normal operating data that can be used as input to create the pattern recognition model. Once the models are calibrated for normal operation, the hybrid model is suitable for use in continuous online monitoring. During online monitoring, new plant operating data is processed first by the heat balance model and then by the pattern recognition model. Results from the pattern recognition model quantify the deviation of each measured or derived parameter from its expected value in normal operation. The hybrid models can detect abnormal changes in plant operating data with very high accuracy and sensitivity. When abnormal behavior is detected, alerts are generated automatically for evaluation by the plant monitoring staff. The new hybrid solution product was developed and verified in the performance of the project. The hybrid solution was tested first in a simulation environment that mimicked the plant data systems and infrastructure used by U.S. power generating plants and utilities. The hybrid solution was then deployed for real-time, online monitoring of an operating coal-fueled power plant at a field test site. Field testing demonstrated that all hybrid solution development objectives were accomplished. The project work was based on combining the capabilities of two existing software products to create the new hybrid solution product. One of these was the existing MapEx® heat balance product and the other was the existing SureSense® advanced pattern recognition product. Each of these separate products was assessed to be at a Technology Readiness Level (TRL) of 9 at the start of the effort. The hybrid solution product was assessed to be at a TRL of 2 at the start of the project based on early feasibility work by the project team. At completion of the field testing performed in the project, the hybrid solution product was assessed to be at a TRL of 7. The project team expects that the hybrid solution product will be deployed commercially and will achieve a TRL of 9 within one year after completion of the project.

01 COAL, LIGNITE, AND PEAT↗