Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Taylor approximation”

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 217 records · Page 12

Summary of Apollo and Lunar Logistics System Plans

The basic mission objective of Project Apollo is to land men on the Moon and return them to Earth at the earliest practicable date. The Apollo crew will consist of three men, two of whom will land on the surface of the Moon, conduct surface operations for up to 24 hr, and then rejoin the third crew member in lunar orbit for return to Earth. Initial Apollo spacecraft capabilities will require the early landings to be within +or-lO deg of the lunar equator on the visible side of the Moon, with preference for landing sites in the leading quadrant (between 270 and 360 deg lunar longitude). As presently planned, the Apollo spacecraft will be capable of carrying approximately 200 lb of scientific equipment to the lunar surface and of bringing approximately 80 lb of lunar material back to Earth. A detailed plan for utilization of crew capabilities while on the lunar surface is not expected to be complete for some time. The first Apollo lunar mission is now scheduled for the late 1960's with additional launches planned at reasonable intervals. i

Taylor, W. B.↗

Visual-Stratigraphic Dating of the GISP2 Ice Core: Basis, Reproducibility, and Application

Annual layers are visible in the Greenland Ice Sheet Project 2 ice core from central Greenland, allowing rapid dating of the core. Changes in bubble and grain structure caused by near-surface, primarily summertime formation of hoar complexes provide the main visible annual marker in the Holocene, and changes in "cloudiness" of the ice correlated with dustiness mark Wisconsinan annual cycles; both markers are evident and have been intercalibrated in early Holocene ice. Layer counts are reproducible between different workers and for one worker at different times, with 1% error over century-length times in the Holocene. Reproducibility is typically 5% in Wisconsinan ice-age ice and decreases with increasing age and depth. Cumulative ages from visible stratigraphy are not significantly different from independent ages of prominent events for ice older than the historical record and younger than approximately 50,000 years. Visible observations are not greatly degraded by "brittle ice" or many other core-quality problems, allowing construction of long, consistently sampled time series. High accuracy requires careful study of the core by dedicated observers.

Alley, R. B.↗

Power series expansions for the frequency and period of the limit cycle of the van der Pol equation

An equation reported by van der Pol (1926) in connection with relaxation-oscillations studies is considered. The equation contains the factor epsilon which can assume values in the range from zero to infinity. The period T(epsilon), or equivalently the frequency nu(epsilon) of the limit cycle has been studied. However, to date there has been little success in discovering the analytical structure of T(epsilon) as a function of epsilon. The present investigation has the objectives to present the Taylor series expansion of nu(epsilon), to locate the singularities which determine the radius of convergence of that expansion, to introduce a new damping variable in terms of which the expansion converges for all epsilon, to form a new expansion for the period T(epsilon) which improves the rate of convergence of the series, to attempt to 'complete' the series, and to compare the obtained results with the numerically determined values of T(epsilon) and with the asymptotic approximation valid for large epsilon.

Andersen, C. M.↗

Theoretical studies of the potential surface for the F - H2 greater than HF + H reaction

The F + H2 yields HF + H potential energy hypersurface was studied in the saddle point and entrance channel regions. Using a large (5s 5p 3d 2f 1g/4s 3p 2d) atomic natural orbital basis set, a classical barrier height of 1.86 kcal/mole was obtained at the CASSCF/multireference CI level (MRCI) after correcting for basis set superposition error and including a Davidson correction (+Q) for higher excitations. Based upon an analysis of the computed results, the true classical barrier is estimated to be about 1.4 kcal/mole. The location of the bottleneck on the lowest vibrationally adiabatic potential curve was also computed and the translational energy threshold determined from a one-dimensional tunneling calculation. Using the difference between the calculated and experimental threshold to adjust the classical barrier height on the computed surface yields a classical barrier in the range of 1.0 to 1.5 kcal/mole. Combining the results of the direct estimates of the classical barrier height with the empirical values obtained from the approximation calculations of the dynamical threshold, it is predicted that the true classical barrier height is 1.4 + or - 0.4 kcal/mole. Arguments are presented in favor of including the relatively large +Q correction obtained when nine electrons are correlated at the CASSCF/MRCI level.

Bauschlicher, Charles W., Jr.↗

Laser Doppler velocity measurements of swirling flows with upstream influence

Swirling flow in a rotating tube is studied by flow visualization at a moderate Reynolds number, and its velocity field is measured by laser-Doppler anemometry. The tube has constant diameter, and approximately uniform initial rigid rotation of the flow is assured by passing the flow through a rotating plug of porous metal before it enters the test section. At moderate swirl values, an object mounted on the tube centerline causes a closed bubble to form upstream of the obstacle, with a clearly defined stagnation point on the axis, and recirculating flow inside the bubble. The bubble length grows upstream as the swirl is increased, until it breaks up into a Taylor column reaching all the way upstream and downstream at swirl values above a certain critical value. A vortex jump (in the sense of Benjamin) occurs downstream of the obstacle except when the Taylor column is present. Using a laser-Doppler anemometer, axial and swirl velocity profiles are obtained at several stations upstream and downstream of the bubble, and in and around the bubble.

Rloff, K. L.↗

Ground-Support Algorithms for Simulation, Processing, and Calibration of Barnes Static Earth Sensor Measurements: Applications to Tropical Rainfall Measuring Mission Observatory

New algorithms are described covering the simulation, processing, and calibration of penetration angles of the Barnes static Earth sensor assembly (SESA) as implemented in the Goddard Space Flight Center Flight Dynamics Division ground support system for the Tropical Rainfall Measuring Mission (TRMM) Observatory. The new treatment involves a detailed analysis of the measurements by individual quadrants. It is shown that, to a good approximation, individual quadrant misalignments can be treated simply as penetration angle biases. Simple formulas suitable for real-time applications are introduced for computing quadrant-dependent effects. The simulator generates penetration angles by solving a quadratic equation with coefficients uniquely determined by the spacecraft's position and the quadrant's orientation in GeoCentric Inertial (GCI) coordinates. Measurement processing for attitude determination is based on linearized equations obtained by expanding the coefficients of the aforementioned quadratic equation as a Taylor series in both the Earth oblateness coefficient (alpha approx. 1/150) and the angle between the pointing axis and the geodetic nadir vector. A simple formula relating a measured value of the penetration angle to the deviation of the Earth-pointed axis from the geodetic nadir vector is derived. It is shown that even near the very edge of the quadrant's Field Of View (FOV), attitude errors resulting from quadratic effects are a few hundredths of a degree, which is small compared to the attitude determination accuracy requirement (0.18 degree, 3 sigma) of TRMM. Calibration of SESA measurements is complicated by a first-order filtering used in the TRMM onboard algorithm to compute penetration angles from raw voltages. A simple calibration scheme is introduced where these complications are avoided by treating penetration angles as the primary raw measurements, which are adjusted using biases and scale factors. In addition to three misalignment parameters, the calibration state vector contains only two average penetration angle biases (one per each pair of opposite quadrants) since, because of the very narrow sensor FOV (+/- 2.6 degrees), differences between biases of the penetration angles measured by opposite quadrants cannot be distinguished from roll and pitch sensor misalignments. After calibration, the estimated misalignments and average penetration angle biases are converted to the four penetration angle biases and to the yaw misalignment angle. The resultant biases and the estimated scale factors are finally used to update the coefficients necessary for onboard computations of penetration angles from measured voltages.

Natanson, G. A.↗

Irregularities in the secular variation and geodynamic implications; Proceedings of the Session, Cincinnati, OH, May 17, 1984

Consideration is given to: variations in the Gauss coefficients of the geomagnetic potential over the last several hundred years; eccentric geomagnetic dipole drift; and evidence for geomagnetic jerks from 1931 to 1971. Among other topics discussed are: models of the geomagnetic field in western Europe from 1960 to 1980; the external and internal parts of the geomagnetic jerk of 1970; secular variation of the magnetic mean energy density at the source layer depth; and motions at the core surface in the geostrophic approximation. Consideration is also given to: the unpredictability of geomagnetic secular variation; the use of short-term core-mantle coupling and geomagnetic variation impulses as Lagrangian tracers of core motions; and a comparison of two sequential geomagnetic polarity transitions in the upper Olduvai and the lower Jarmillio in the Southern Hemisphere.

Taylor, P.↗

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗

Electrically conductive palladium containing polyimide films

Lightweight, high temperature resistant, electrically conductive, palladium containing polyimide films and methods for their preparation are described. A palladium (II) ion-containing polyamic acid solution is prepared by reacting an aromatic dianhydride with an equimolar quantity of a palladium II ion-containing salt or complex and the reactant product is cast as a thin film onto a surface and cured at approximately 300 C to produce a flexible electrically conductive cyclic palladium containing polyimide. The source of palladium ions is selected from the group of palladium II compounds consisting of LiPdCl4, PdS(CH3)2Cl2Na2PdCl4, and PdCl2. The films have application to aerodynamic and space structures and in particular to the relieving of space charging effects.

Taylor, L. T.↗

The Apollo 17 mare basalts: Serenely sampling Taurus-Littrow

As we are all aware, the Apollo 17 mission marked the final manned lunar landing of the Apollo program. The lunar module (LM) landed approximately 0.7 km due east of Camelot Crater in the Taurus-Littrow region on the southwestern edge of Mare Serenitatis. Three extravehicular activities (EVA's) were performed, the first concentrating around the LM and including station 1 approximately 1.1 km south-southeast of the LM at the northwestern edge of Steno Crater. The second traversed approximately 8 km west of the LM to include stations 2, 3, 4, and 5, and the third EVA traversed approximately 4.5 km to the northwest of the LM to include stations 6, 7, 8, and 9. This final manned mission returned the largest quantity of lunar rock samples, 110.5 kg/243.7 lb, and included soils, breccias, highland samples, and mare basalts. This abstract concentrates upon the Apollo 17 mare basalt samples.

Neal, Clive R.↗

On the Universality of the Kolmogorov Constant in Numerical Simulations of Turbulence

Motivated by a recent survey of experimental data, we examine data on the Kolmogorov spectrum constant in numerical simulations of isotropic turbulence, using results both from previous studies and from new direct numerical simulations over a range of Reynolds numbers (up to 240 on the Taylor scale) at grid resolutions up to 512(exp 3). It is noted that in addition to k(exp -5/3) scaling, identification of a true inertial range requires spectral isotropy in the same wavenumber range. We found that a plateau in the compensated three-dimensional energy spectrum at k(eta) approx. = 0.1 - -0.2, commonly used to infer the Kolmogorov constant from the compensated three-dimensional energy spectrum, actually does not represent proper inertial range behavior. Rather, a proper, if still approximate, inertial range emerges at k(eta) approx. = 0.02 - 0.05 when R(sub lambda) increases beyond 140. The new simulations indicate proportionality constants C(sub 1) and C in the one- and three-dimensional energy spectra respectively about 0.60 and 1.62. If the turbulence were perfectly isotropic then use of isotropy relations in wavenumber space (C(sub 1) = 18/55 C) would imply that C(sub 1) approx. = 0.53 for C = 1.62, in excellent agreement with experiments. However the one- and three-dimensional estimates are not fully consistent, because of departures (due to numerical and statistical limitations) from isotropy of the computed spectra at low wavenumbers. The inertial scaling of structure functions in physical space is briefly addressed. Since DNS is still restricted to moderate Reynolds numbers, an accurate evaluation of the Kolmogorov constant is very difficult. We focus on providing new insights on the interpretation of Kolmogorov 1941 similarity in the DNS literature and do not consider issues pertaining to the refined similarity hypotheses of Kolmogorov (K62).

Yeung, P. K.↗

Ignition and Burn in a Hybrid Nuclear Fuel for a Pulsed Rocket Engine

This work explores the parameter space of a cylindrical hybrid nuclear fuel in support of a z-pinch driven pulsed fission-fusion (PuFF) engine. 0D power balance and 1D burn wave calculations have been performed to explore the parameter space of hybrid cylindrical nuclear fuels. The boundary of minimal initial conditions needed to reach breakeven are found within the context of the model. The effects of initial conditions upon the yield at the end of burn wave expansion are also determined. The model is used to examine the minimum initial energies predicted to result in yields of a few MJ. The goal of this work is to guide fuel design, inform future models and experiments as well as look for the most efficient parameter space for ignition in a z-pinch driven hybrid nuclear reaction. The impact of initial parameters upon ignition, burn, and gain are discussed. It is found that a hybrid cylindrical target may breakeven with initial energy near the axis of approximately 4 to 6 MJ in lithium deuteride/uranium 235 fuel. It is also found that magnetic field can lower the threshold further of which the magnitude changes across the parameter space. The dual fusion/fission reactions are found to boost each other leading to lower initial driving energies needed to reach breakeven in the hybrid cylindrical nuclear fuel.

fission↗

Interpretation of Mariner 10 infrared observations of Venus

The infrared radiometer experiment on Mariner 10 measured limb-darkening curves for Venus in two spectral intervals, one near 11 microns and the other near 45 microns. These are analyzed in terms of the vertical opacity profile at each wavelength over a limited altitude range, approximately 60 to 80 km above the surface of the planet. Accurate multiple-scattering calculations are used to show that both opacity profiles are consistent with a model containing a cloud of sulphuric acid droplets with radii of 1.1 microns and a small amount of water vapor. Profiles of particle number density and humidity vs height are presented.

Taylor, F. W.↗

Stress intensity factors for long, deep surface flaws in plates under extensional fields

Using a singular solution for a part circular crack, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50 and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the ''equivalent'' semi-elliptical flaw results was not valid for a/2c less than 0.20. Best overall agreement for the moderate (a/t approximately 0.5) to deep flaws (a/t approximatelly 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory, when compared on the basis of equivalent flaw depth and area.

Harms, A. E.↗

Effect of a crystal-melt interface on Taylor-vortex flow

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal-melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two-phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two-phase system is given by the classical results for a rigid-walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow-gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two-phase system becomes less stable as the finite gap tends to the narrow-gap limit. The two-phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n = 1; the stability of these n = 1 modes is sensitive to the latent heat of fusion.

Mcfadden, G. B.↗

Window Cooling Studies and Disk Vibration Testing on a Subset of Mo-100 Disks

Production of metastable Technetium-99 (Tc-99m), a radioactive tracer that emits gamma rays, is vital to the medical imaging community. Tc-99m is extracted from the decay of Molybdenum-99 (Mo-99) which has a half-life of about 2-3 days. The work presented in this report is part of the NNSA’s mission to produce Mo-99 commercially, within the US, without the use of highly enriched uranium (HEU) in support of nonproliferation and global security. Los Alamos National Laboratory (LANL) is working with NorthStar Medical Radioisotopes (NMR) on their efforts to produce Mo-99 through the irradiation of Mo-100 targets using an electron beam. The NMR target comprises a stack of approximately 60-70 Mo-100 disks with diameter 24 mm and thickness 0.74 mm held in stainless steel laminations, each separated using 0.25 mm thick stainless-steel spacers. The symmetric target stack is housed in an Inconel vessel with two Inconel windows on either side. Two electron accelerators are used to produce 40 MeV, 3.16 µA electron beams each that penetrate the Inconel windows and irradiate the Mo-100 disks. Approximately 90% of the total 250 kW beam power is deposited in the NMR target during the irradiation process, with a smaller percentage adding up to 2.2 kW of heat deposited on the Inconel window. During irradiation, pressurized helium gas flows through thin gaps between the disks cooling the beam window, target disks, disk laminations and spacers. Both NMR and LANL have found during cold testing of the target system (no heat deposition) that the Mo 100 disks undergo significant mass loss and disk breakage due to vibrations induced by the flowing helium gas. The mass loss is not only undesirable due to monetary loss from reduced final quantities of Mo-99, but also due to the hazards associated with radioactive material trapped in the cooling lines and particle filters. The effect of flow rate and target geometry on the flow induced vibrations need to be quantified, and recommendations provided to minimize this mass loss. LANL has previously also tested NMR’s Inconel beam window by heating the window, while flowing pressurized helium, using the average heat deposited on the window. However, the NMR beam is pulsed with a duty cycle of 12.5%, which introduces oscillation in temperature around the nominal 600 °C steady state value with each pulse. Available fatigue curves for Inconel are few, established for room temperature, and they are based on mechanical strain cycles not thermally induced strain as in the NMR target. The effect of pulsed beam heating on the Inconel window therefore needs to be quantified. This report details the experiments conducted to assess the factors that lead to mass loss in the NMR target disks as well as to understand the effect of a pulsed beam on NMR’s Inconel window. This work describes LANL’s experimental characterization of the flow induced vibrations and disk mass loss in a reduced scale set-up containing 5 to 10 Mo-100 disks. We use high speed imaging, displacement measurements and microphone measurements combined with signal processing to estimate the vibration frequency of each disk. The effect of disk thickness, target fit and duration of testing on the mass loss is described. We find that in the current configuration of NMR targets, the vibrations and mass loss on the first disk are minimized, while those in the adjacent disks are highest. The microphone and high-speed image data show that increased flow rates and increased duration of testing increases vibration frequency and mass loss. The mass loss is due to both disk rotation and back and forth motion. There are visible wear marks on the disks with the highest mass loss. We also note that the current NMR window gap reduces flow induced vibrations compared to the previous smaller gaps. Improved target holders significantly reduce disk mass loss to almost negligible quantities. This work finds that the larger window to first disk gap and improved target holder geometry should allow NMR to successfully conduct irradiations with minimal mass loss. The window tests were conducted to understand the effect of a pulsed beam on both the window longevity and to estimate the window temperature and displacement during pulsing. The experiments presented here were performed at significantly low power, due to the limitations of the induction heating system. The window temperature rose to approximately 73 °C with a significantly reduced power of 45 W without beam pulsing. With a 5 Hz pulse rate, 12.5% duty cycle, the window temperature remained constant at 26 °C. These experiments will be repeated with improved coil geometry and reported in upcoming journal papers.

42 ENGINEERING↗

Determination of an angle of attack sensor correction for a general aviation airplane at large angles of attack as determined from wind tunnel and flight tests

A comprehensive investigation into the flow correction for an angle of attack sensor mounted ahead of the wing tip of a general aviation research airplane has been conducted at the Langley Research Center. This correction has been determined in wind tunnels using a full-scale model up to angles of attack of 45 deg and a 1/5-scale model up to 80 deg angle of attack. The flow correction has also been obtained in flight by using a standard technique at low angles of attack and in spinning flight at larger angles of attack, by using both a simple approximate technique and a parameter estimation technique. The results show the correction is significant, reaching 10 deg at a measured angle of attack of about 90 deg. The flow correction was sensitive to the angle of sideslip at measured angles of attack greater than 60 deg and was not influenced by wing leading-edge modifications or aileron deflections.

Moul, T. M.↗

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Whitfield, David L.↗