Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EXPONENTIAL FUNCTION”

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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Advanced Unstructured Grid Generation for Complex Aerodynamic Applications

A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.

Pirzadeh, Shahyar↗
NASA NTRS2003

Rapid Acceleration of a Coronal Mass Ejection in the Low Corona and Implications of Propagation

A high-velocity Coronal Mass Ejection (CME) associated with the 2002 April 21 X1.5 flare is studied using a unique set of observations from the Transition Region and Coronal Explorer (TRACE), the Ultraviolet Coronagraph Spectrometer (UVCS), and the Large-Angle Spectrometric Coronagraph (LASCO). The event is first observed as a rapid rise in GOES X-rays, followed by simultaneous conjugate footpoint brightenings connected by an ascending loop or flux-rope feature. While expanding, the appearance of the feature remains remarkably constant as it passes through the TRACE 195 A passband and LASCO fields-of-view, allowing its height-time behavior to be accurately determined. An analytic function, having exponential and linear components, is found to represent the height-time evolution of the CME in the range 1.05-26 R. The CME acceleration rises exponentially to approx. 900 km/sq s within approximately 20-min, peaking at approx.1400 m/sq s when the leading edge is at approx. 1.7 R. The acceleration subsequently falls off as a slowly varying exponential for approx.,90-min. At distances beyond approx. 3.4 R, the height-time profile is approximately linear with a constant velocity of approx. 2400 km/s. These results are briefly discussed in light of recent kinematic models of CMEs.

Gallagher, Peter T.↗
NASA NTRS2019

Lightning Strike Distance Distribution Beyond a Preexisting Lightning Area

The 45th Weather Squadron (45 WS) asked the Applied Meteorology Unit (AMU) to review the 30-year-old, lightning stand-off distances of 5 nautical miles (nmi) for applicability to today's operations. This was based on the realization that previous lightning strike distance studies did not match how 45 WS issues lightning warnings (Roeder, 2008). The previous lightning distance studies were from the point of origin of the lightning or the average starting location that would tend to be in the core of the thunderstorm. However, the 45 WS issues lightning warnings based on the edge of a preexisting lightning area. Before beginning the AMU project, it took several years to develop a method to calculate a distance distribution beyond a preexisting area (Roeder, 2015). The AMU pulled Lightning Detection and Ranging (LDAR) sensor data from 1/1/2013 to 12/31/2013. This dataset consisted of 37 million individual source data points from the LDAR sensors. Only sources within 50 km north, south, east or west of the LDAR grid center were included in the dataset. This limited the use of LDAR data to that with the greatest accuracy of source detection and increased data processing. Points were grouped into flashes based on spatial and temporal criteria. Based on the sensitivity analysis the AMU performed on the flash clustering algorithm, a time value of 0.3 seconds was found to model flashes adequately. Distance parameters were tested from 1,500 to 7,500 meters (m) in 500 m increments. Distance parameters of both 3,000 m and 4,000 m produced results in the plotting tool that were most representative of the physical behavior of lightning. Thus statistics were gathered for the most representative of these spatial and temporal criteria on the flash size and the polygon expansion distance in order to find the correct data distributions. The best fit curves for the LDAR polygon expansion frequency vs. distances for both the 3 kilometer (km) and 4 km distance threshold values were exponential decay functions and had R2 values of > 0.998, indicating good model fits. The equations of the best fit curves were then used to calculate a desired safety radius of 4 nmi for either 3 km or 4 km distance threshold criteria. The AMU analysis concludes the safe reduction of the 5 nmi lightning warning circles to 4 nmi should improve the operational impact by 36% if based on distance from the center of the property area being protected. If based on the edge of the property being protected, then the reduction is 4.5 nmi to 4 nmi and the operational impact is decreased by 21%. For the 6 nmi lightning warning circles, the recommended 4 nmi stand-off distance will result in a safe reduction of operational impact of 31% if based on the center of the area being protected, or 16% if based on the edge of the property.

Flash clustering algorithm↗
NASA NTRSDate not supplied

Analysis of Oxygen Liquefaction with Transient Flow Rates for ISRU Systems

Human occupation of lunar and Martian surfaces requires in-situ resource utilization (ISRU) to create a sustainable environment with the limited resources available in space. Fuel and oxidizer generation is essential for developing a refueling capability for spacecraft, significantly reducing the propellant mass required for landing. Liquefaction systems are a key step in producing and storing cryogenic liquids such as oxygen, hydrogen, and methane. All those fluids are critical to propulsion, life support, and other spacecraft systems. NASA has previously confirmed the presence of water on the Moon and an electrolysis process can be used to separate the oxygen from the hydrogen molecules. Oxygen has also been found within lunar regolith and can be separated through ISRU processes. The extracted oxygen gas can then be liquefied inside a storage tank with tube-on-tank heat exchangers for future use as an oxidizer for propellants. While steady state liquefaction performance is easy to model, power limitations and cyclical environments caused by the change in Sun exposure between day and night periods potentially call for transient operations. The following analysis was performed using the Thermal Desktop software to investigate how various transient gaseous oxygen (GOX) flow rates impact the production and storage of liquid oxygen (LOX) in a 1-g liquefaction system. Variations of sinusoidal and exponential step functions were selected to model potential GOX flow rates that could be experienced by ISRU systems on lunar or Martian surfaces. This early computational analysis provides some insight on how transient operations impact oxygen liquefaction systems and helps illustrate operational questions to explore experimentally throughout the design process.

Cryogenic Fluid Management↗
NASA NTRS2023

Modeling holes and voids in three dimensions using a single element within the Extended Finite Element framework

This paper introduces a highly efficient computational approach using the extended finite element method to model three-dimensional mechanics of holes and voids. The defect is encapsulated within a single element with a tailored exponential enrichment function that captures the behavior near the discontinuity boundary and can account for the pressure acting on the void’s surface through an equivalent nodal force vector. The method’s results were compared against analytical solutions and conventional finite element method results for problems involving single and multiple holes. The comparison demonstrated that the method provides accurate stress concentration estimates while adhering to computational constraints.

Adnan Shahriar↗
DOE OSTI2017

Plasma Heating in Solar Microflares: Statistics and Analysis

In this paper we present the results of an analysis of 481 weak solar flares, from A0.01 class flares to the B GOES class, that were observed during the period of extremely low solar activity from 2009 April to July. For all flares we measured the temperature of the plasma in the isothermal and two-temperature approximations and tried to fit its relationship with the X-ray class using exponential and power-law functions. We found that the whole temperature distribution in the range from A0.01 to X-class cannot be fit by one exponential function. The fitting for weak flares below A1.0 is significantly steeper than that for medium and large flares. The power-law approximation seems to be more reliable: the corresponding functions were found to be in good agreement with experimental data both for microflares and for normal flares. Our study predicts that evidence of plasma heating can be found in flares starting from the A0.0002 X-ray class. Weaker events presumably cannot heat the surrounding plasma. We also estimated emission measures for all flares studied and the thermal energy for 113 events.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1979

Study on the application of NASA energy management techniques for control of a terrestrial solar water heating system

This paper addresses the potential for enhanced solar system performance through sophisticated control of the collector loop flow rate. Computer simulations utilizing the TRNSYS solar energy program were performed to study the relative effect on system performance of eight specific control algorithms. Six of these control algorithms are of the proportional type: two are concave exponentials, two are simple linear functions, and two are convex exponentials. These six functions are typical of what might be expected from future, more advanced, controllers. The other two algorithms are of the on/off type and are thus typical of existing control devices. Results of extensive computer simulations utilizing actual weather data indicate that proportional control does not significantly improve system performance. However, it is shown that thermal stratification in the liquid storage tank may significantly improve performance.

Swanson, T. D.↗
NASA NTRS1994

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Gottlieb, David↗
NASA NTRS1987

Strain energy release rates of composite interlaminar end-notch and mixed-mode fracture: A sublaminate/ply level analysis and a computer code

A computer code is presented for the sublaminate/ply level analysis of composite structures. This code is useful for obtaining stresses in regions affected by delaminations, transverse cracks, and discontinuities related to inherent fabrication anomalies, geometric configurations, and loading conditions. Particular attention is focussed on those layers or groups of layers (sublaminates) which are immediately affected by the inherent flaws. These layers are analyzed as homogeneous bodies in equilibrium and in isolation from the rest of the laminate. The theoretical model used to analyze the individual layers allows the relevant stresses and displacements near discontinuities to be represented in the form of pure exponential-decay-type functions which are selected to eliminate the exponential-precision-related difficulties in sublaminate/ply level analysis. Thus, sublaminate analysis can be conducted without any restriction on the maximum number of layers, delaminations, transverse cracks, or other types of discontinuities. In conjunction with the strain energy release rate (SERR) concept and composite micromechanics, this computational procedure is used to model select cases of end-notch and mixed-mode fracture specimens. The computed stresses are in good agreement with those from a three-dimensional finite element analysis. Also, SERRs compare well with limited available experimental data.

Valisetty, R. R.↗
DOE OSTI2013

Neutron light output response and resolution functions in EJ-309 liquid scintillation detectors

Here, the neutron light output response functions and detector resolution functions were measured at Ohio University's tandem Van de Graaff generator for three cylindrical EJ-309 liquid scintillator cells, having dimensions 12.7(circle divide)-by-12.7, 7.6-by-7.6, and 7.6-by-5.1 cm. A 7.44 MeV deuteron beam was used on an Al-27 target generating a continuous spectrum over the energy range from a few hundred keV to over 10 MeV. The light output response functions are determined using an exponential fit. Detector resolution functions are obtained for the 12.7-by-12.7 and 7.6-by-7.6 cm detectors. It is demonstrated that the dependence on detector size is important for the light output response functions, but not to the same extent for the resolution function, even when photomultiplier tubes, detector material, and other detector characteristics are carefully matched.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1989

Responsivity variations in the IRAS survey

The IRAS survey detectors show nonlinear characteristics in their gains and baselines. This behavior can be described by an exponentially decaying gain enhancement, dependent on previously observed flux. The baseline behavior has been modeled by a decaying function composed of the sum of two exponential functions. The scale lengths are 10 arcmin and 1.1 deg for 12 microns, and 8 arcmin and 43 arcmin for 25 microns. Amplitude changes due to this type of hysteresis are less than 1 percent. In addition there is a considerable response of all detectors to particles associated with the South Atlantic Anomaly. Attempts to correct for this effect were performed on the 12- , 60- and 100-micron detectors in the form of bias boosts. This note presents a correction procedure for the 25-micron detectors.

Deul, E. R.↗
NASA NTRS1969

Simple quasi-exponential slope generator

Circuitry for digitally generating an exponentially decaying wave function permits discrete values to be sampled from the exponential waveform for comparison with a binary number of specified accuracy. This exponential-decay generator employs a simple binary counter to count in the sequence of exponential decay.

Anderson, T. O.↗
NASA NTRS1978

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Brandt, A.↗
DOE OSTI2021

Cryogenic operation of planar ultrananocrystalline diamond field emission source in SRF injector

Here, we report a demonstration of electron beam generation in a superconducting radio frequency (SRF) Teraelectronvolt Energy Superconducting Linear Accelerator 1.3 GHz gun equipped with a field emission cathode and operated at 2 K. The cathode is a submicrometer film of nitrogen-incorporated ultrananocrystalline diamond [(N)UNCD] deposited atop a Nb RRR300 cathode plug that is 4 mm in diameter. Measurements of the output current showed that it increased exponentially as a function of the gun gradient. Our results demonstrate a feasible path toward simplified fully cryogenic SRF injector technology. At a maximal gradient of 0.9 MV/m, a current density of 22 μA/cm2 was obtained [calculated as a 2.75 μA current over the total cathode surface area of π(2 mm)2]. One important finding is that the electron emitter made of (N)UNCD, a material long been known as a highly efficient field emission material, demonstrated a record low turn-on gradient of 0.6 MV/m. A hypothesis explaining this behavior is proposed.

43 PARTICLE ACCELERATORS↗
NASA NTRS1992

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Gottlieb, David↗
DOE OSTI2017

Semi-empirical scaling for ion–atom single charge exchange cross sections in the intermediate velocity regime

We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities from ${10}^{7}\,{\rm{t}}{\rm{o}}\,{10}^{9}\,\mathrm{cm}\,{{\rm{s}}}^{-1}$ and ions with positive charge $q\lt 8$. Non-resonant cross sections tend to have a velocity peak at collision velocities $v\lesssim 1\ {\rm{a}}{\rm{u}}$ with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m , is proportional to the energy defect of the collision, ${\rm{\Delta }}E$, which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T , and inversely proportional to v m . For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters ${v}_{{\rm{m}}},{I}_{{\rm{T}}},{Z}_{{\rm{T}}},\mathrm{and}\ {Z}_{{\rm{P}}}$, where the ${Z}_{{\rm{T}},{\rm{P}}}$ are the target and projectile atomic numbers. In conclusion, for the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1993

Specular scattering on a terrestrial playa and implications for planetary surface studies

Multiangle Advanced Solid State Array Spectroradiometer (ASAS) and Portable Apparatus for Rapid Acquisition of Bidirectional Observations of Land and Atmosphere (PARABOLA) visible and near infrared reflectance data covering the Lunar Lake playa, Nevada, were modeled using specular and volume scattering theory. The volume component used to model the data was based on the Hapke (1986) model and the specular scattering component was based on Fresnel reflection from surface facets with a distribution of tilts. Specular scattering was needed to explain the several-fold increase in reflectance observed at high phase angles in the solar principal plane. Results imply single scattering albedos of approximately 0.93 to 0.95, a real index of refraction value of approximately 1.52 (at a wavelength of 0.66 micron), a small imaginary index of refraction and an exponential facet tilt probability function for the playa. Electron micrographs showed th playa surface to consist of ensembles of smooth, micrometer-scale ellipsoidal particles on gently undulating topography at the millimeter to centimeter scale. The exponential probability function is consistent with this observation. Mars and the icy satellites are discussed as possible places to look for a significant specular scattering component.

Shepard, Michael K.↗
NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗