Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable coefficients”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Modeling Turbulent Combustion for Variable Prandtl and Schmidt Number

This report consists of two abstracts submitted for possible presentation at the AIAA Aerospace Science Meeting to be held in January 2005. Since the submittal of these abstracts we are continuing refinement of the model coefficients derived for the case of a variable Turbulent Prandtl number. The test cases being investigated are a Mach 9.2 flow over a degree ramp and a Mach 8.2 3-D calculation of crossing shocks. We have developed an axisymmetric code for treating axisymmetric flows. In addition the variable Schmidt number formulation was incorporated in the code and we are in the process of determining the model constants.

Hassan, H. A.↗
NASA NTRS2008

Vertical Jump Height is more Strongly Associated with Velocity and Work Performed Prior to Take-off

Vertical jump (VJ) height is commonly used as a measure of athletic capability in strength and power sports. Although VJ has been shown to be a predictor of athletic performance, it is not clear which kinetic ground reaction force (GRF) variables, such as peak force (PF), peak power (PP), peak velocity (PV), total work (TW) or impulse (Imp) are the best correlates. To determine which kinetic variables (PF, PP, PV, TW, and Imp) best correlate with VJ height. Twenty subjects (14 males, 6 females) performed three maximal countermovement VJs on a force platform (Advanced Mechanical Technology, Inc., Watertown, MA, USA). VJ jump height was calculated as the difference between standing reach and the highest reach point measured using a Vertec. PF, PP, PV, TW, and Imp were calculated using the vertical GRF data sampled at 1000 Hz from the lowest point in the countermovement through the concentric portion until take-off. GRF data were normalized to body mass measured using a standard scale (Detecto, Webb City, MO, USA). Correlation coefficients were computed between each GRF variable and VJ height using a Pearson correlation. VJ height (43.4 plus or minus 9.1 cm) was significantly correlated (p less than 0.001) with PF (998 plus or minus 321 N; r=0.51), PP (1997 plus or minus 772 W; r=0.69), PV (2.66 plus or minus 0.40 m (raised dot) s(sup -1); r=0.85), TW (259 plus or minus 93.0 kJ; r=0.82), and Imp (204 plus or minus 51.1 N(raised dot)s; r=0.67). Although all variables were correlated to VJ height, PV and TW were more strongly correlated to VJ height than PF, PP, and Imp. Therefore, since TW is equal to force times displacement, the relative displacement of the center of mass along with the forces applied during the upward movement of the jump are critical determinants of VJ height. PV and TW are key determinants of VJ height, and therefore successful training programs to increase VJ height should focus on rapid movement (PV) and TW by increasing power over time rather than focusing on PF alone.

Bentley, J. R.↗
NASA NTRS2005

Qualifying a Bonding Process for the Space Interferometry Mission

The Space Interferometry Mission consists of three parallel Michelson interferometers that will be capable of detecting extrasolar planets with a high degree of accuracy and precision. High levels of stability must be met in order to fulfill the scientific requirements of this mission. To attain successful measurements the coefficient of thermal expansion between optics and bonding material must be minimized without jeopardizing the integrity of the bonds. Optic-to-optic bonds have been analyzed to better understand variables such as the effects of the coefficient of thermal expansion differences between optics and bonding materials, and materials have been chosen for the project based on these analyses. A study was conducted to determine if a reliable, repeatable process for bonding by wicking adhesive could be obtained using a low-viscosity epoxy and ultra-low expansion glass. A process of creating a methodology of bonding fused silica optics with Z-6020 silane primer and Epo-Tek 301 epoxy will be discussed.

Joyce, Gretchen P.↗
NASA NTRS1992

Reduced basis technique for calculating sensitivity coefficients of nonlinear structural response

An efficient reduced basis technique is presented for calculating the sensitivity of nonlinear structural response to variations in the design variables. The structure is discretized by using two-field mixed finite element models. The vector of structural response and its sensitivity coefficients (derivatives with respect to design variables) are each expressed as a linear combination of a small number of basis (or global approximation) vectors. The Bubnov-Galerkin technique is then used to approximate each of the finite element equations governing the response and the sensitivity coefficients by a small number of algebraic equations in the amplitudes of these vectors. The path derivatives (derivatives of the response vector with respect to path parameters, e.g., load parameters) are used as basis vectors for approximating the response. A combination of the path derivatives and their derivatives with respect to the design variables is used for approximating the sensitivity coefficients. The potential of the proposed technique is discussed and its effectiveness is demonstrated by means of numerical examples of laminated composite plates subjected to mechanical and thermal loads.

Noor, Ahmed K.↗
NASA NTRS1972

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗
NASA NTRS1979

Relationship of red and photographic infrared spectral radiances to alfalfa biomass, forage water content, percentage canopy cover, and severity of drought stress

Red and photographic infrared spectral data were collected using a handheld radiometer for two cuttings of alfalfa. Significant linear and non-linear correlation coefficients were found between the spectral variables and plant height, biomass, forage water content, and estimated canopy cover for the earlier alfalfa cutting. The alfalfa of later cutting experienced a period of severe drought stress which limited growth. The spectral variables were found to be highly correlated with the estimated drought scores for this alfalfa cutting.

Tucker, C. J.↗
NASA NTRS1980

Relationship of crop radiance to alfalfa agronomic values

Red and photographic infrared spectral data of alfalfa were collected at the time of the third and fourth cuttings using a hand-held radiometer for the earlier alfalfa cutting. Significant linear and non-linear correlation coefficients were found between the spectral variables and plant height, biomass, forage water content, and estimated canopy cover. For the alfalfa of the later cutting, which had experienced a period of severe drought stress which limited growth, the spectral variables were found to be highly correlated with the estimated drought scores.

Tucker, C. J.↗
NASA NTRS1985

The OH + HBr reaction revisited

Variable-temperature measurements of the rate coefficient /k(1)/ for the reaction OH + HBr yield Br + H2O are presented. The measurements are verified by two techniques: one involved a 266-nm pulsed-laser photolysis of O3/H2O/HBr/He mixtures in conjunction with time-resolved resonance fluorescence detection of OH, the second comprised pulsed laser-induced fluorescence detection of OH following 248-nm pulsed-laser photolysis of H2O2/HBr/Ar mixtures. It is reported that k(1) = (11.9 + or -1.4 x 10 to the -12th (cu cm)/(molecule)(s) independent of temperature. The measurements are compared with other available results.

Ravishankara, A. R.↗
NASA NTRS1986

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations.

Gottlieb, D.↗
NASA NTRS1986

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

King, H. F.↗
NASA NTRS1989

On estimating total daily evapotranspiration from remote surface temperature measurements

A method for calculating daily evapotranspiration from the daily surface energy budget using remotely sensed surface temperature and several meteorological variables is presented. Vaules of the coefficients are determined from simulations with a one-dimensional boundary layer model with vegetation cover. Model constants are obtained for vegetation and bare soil at two air temperature and wind speed levels over a range of surface roughness and wind speeds. A different means of estimating the daily evapotranspiration based on the time rate of increase of surface temperature during the morning is also considered. Both the equations using our model-derived constants and field measurements are evaluated, and a discussion of sources of error in the use of the formulation is given.

Carlson, Toby N.↗
NASA NTRS1989

Measurement of strains at high temperatures by means of a portable holographic moire camera

Electronic holographic moire is utilized to measure strains at temperatures up to 1000 C. A CW laser operating at 50 mW and at the wavelength of 632.8 nm is used to illuminate the objects under study. The main variables influencing the fringe patterns visibility are discussed and measurements are performed to obtain the values of these variables in the performed experiments. The coefficient of expansion of an alloy is measured at temperatures ranging from 797 C to 986 C. Excellent agreement is found between the measured values and those provided by the manufacturer.

Sciammarella, C. A.↗
NASA NTRS1990

Analytical aerodynamic model of a high alpha research vehicle wind-tunnel model

A 6 DOF analytical aerodynamic model of a high alpha research vehicle is derived. The derivation is based on wind-tunnel model data valid in the altitude-Mach flight envelope centered at 15,000 ft altitude and 0.6 Mach number with Mach range between 0.3 and 0.9. The analytical models of the aerodynamics coefficients are nonlinear functions of alpha with all control variable and other states fixed. Interpolation is required between the parameterized nonlinear functions. The lift and pitching moment coefficients have unsteady flow parts due to the time range of change of angle-of-attack (alpha dot). The analytical models are plotted and compared with their corresponding wind-tunnel data. Piloted simulated maneuvers of the wind-tunnel model are used to evaluate the analytical model. The maneuvers considered are pitch-ups, 360 degree loaded and unloaded rolls, turn reversals, split S's, and level turns. The evaluation finds that (1) the analytical model is a good representation at Mach 0.6, (2) the longitudinal part is good for the Mach range 0.3 to 0.9, and (3) the lateral part is good for Mach numbers between 0.6 and 0.9. The computer simulations show that the storage requirement of the analytical model is about one tenth that of the wind-tunnel model and it runs twice as fast.

Cao, Jichang↗
NASA NTRS1999

Force and Moment Approach for Achievable Dynamics Using Nonlinear Dynamic Inversion

This paper describes a general form of nonlinear dynamic inversion control for use in a generic nonlinear simulation to evaluate candidate augmented aircraft dynamics. The implementation is specifically tailored to the task of quickly assessing an aircraft's control power requirements and defining the achievable dynamic set. The achievable set is evaluated while undergoing complex mission maneuvers, and perfect tracking will be accomplished when the desired dynamics are achievable. Variables are extracted directly from the simulation model each iteration, so robustness is not an issue. Included in this paper is a description of the implementation of the forces and moments from simulation variables, the calculation of control effectiveness coefficients, methods for implementing different types of aerodynamic and thrust vectoring controls, adjustments for control effector failures, and the allocation approach used. A few examples illustrate the perfect tracking results obtained.

Ostroff, Aaron J.↗
NASA NTRS2005

Energy Finite Element Analysis for Computing the High Frequency Vibration of the Aluminum Testbed Cylinder and Correlating the Results to Test Data

The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.

Vlahopoulos, Nickolas↗
NASA NTRS2023

Wheat Crop Traits Conferring High Yield Potential May Also Improve Yield Stability Under Climate Change

Increasing genetic wheat yield potential is considered by many as critical to increasing global wheat yields and production, baring major changes in consumption patterns. Climate change challenges breeding by making target environments less predictable, altering regional productivity and potentially increasing yield variability. Here we used a crop simulation model solution in the SIMPLACE framework to explore yield sensitivity to select trait characteristics (radiation use efficiency [RUE], fruiting efficiency and light extinction coefficient) across 34 locations representing the world’s wheat-producing environments, determining their relationship to increasing yields, yield variability and cultivar performance. The magnitude of the yield increase was trait-dependent and differed between irrigated and rainfed environments. RUE had the most prominent marginal effect on yield, which increased by about 45 % and 33 % in irrigated and rainfed sites, respectively, between the minimum and maximum value of the trait. Altered values of light extinction coefficient had the least effect on yield levels. Higher yields from improved traits were generally associated with increased inter-annual yield variability (measured by standard deviation), but the relative yield variability (as coefficient of variation) remained largely unchanged between base and improved genotypes. This was true under both current and future climate scenarios. In this context, our study suggests higher wheat yields from these traits would not increase climate risk for farmers and the adoption of cultivars with these traits would not be associated with increased yield variability.

Climate change↗
NASA NTRS1980

A computer program for determining truncation error coefficients for Runge-Kutta methods

The basic structure of a program to generate the truncation error coefficients for Runge-Kutta (RK) methods is reformulated to reduce storage requirements significantly and to accommodate variable dimensioning. This FORTRAN program, SUBROUTINE RKEQ, determines truncation error coefficients for RK algorithms for orders 1 through 10 and extends the order of coefficients through 12 with the 11th- and 12th-order terms determined following the patterns used to establish the lower order coefficients. Both subroutines (the original and RKEQ) are also written to treat RK m-fold methods which utilize m known derivatives of f to increase the order of the algorithm. Setting m = 0 gives the classical RK algorithm.

Horn, M. K.↗
NASA NTRS2015

Temperature-Dependent Refractive Index Measurements of Caf2, Suprasil 3001, and S-FTM16 for the Euclid Near Infrared Spectrometer and Photometer

Using the Cryogenic High Accuracy Refraction Measuring System (CHARMS) at NASA's Goddard Space Flight Center, we measured absolute refractive indices at temperatures from 100 to 310 K at wavelengths from 0.42 to 3.6 microns for CaF2, Suprasil 3001 fused silica, and S-FTM16 glass in support of lens designs for the Near Infrared Spectrometer and Photometer (NISP) for ESA's Euclid dark energy mission. We report absolute refractive index, dispersion (dn/dλ), and thermo-optic coefficient (dn/dT) for these materials. In this study, materials from different melts were procured to understand index variability in each material. We provide temperature-dependent Sellmeier coefficients based on our data to allow accurate interpolation of index to other wavelengths and temperatures. For calcium fluoride (CaF2) and S-FTM16, we compare our current measurements with CHARMS measurements of these materials made in the recent past for other programs. We also compare Suprasil 3001's indices to those of other forms of fused silica we have measured in CHARMS.

geometrical optics↗