Search NASA⌕ Search

SEARCH · Search NASA

Results for “Corrected equation”

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 55 records · Page 3

Remotely sensed sea surface temperature variability off California during a 'Santa Ana' clearing

Multichannel atmospheric correction equations for the NOAA 6 proposed by Bernstein (1982) and by McClain (1981) are evaluated by using satellite and in situ data collected over and in the Southern California Bight. The temporal and spatial variation of sea surface temperature over small scales is estimated from the data, and the effect of this variation in matching satellite and in situ data sets is discussed. Changes in the temperature fields between images are examined for diurnal variation and for surface advection of horizontal temperature gradients.

Lynn, R. J.↗

Flux-limited diffusion in hydrodynamics

The radiation transport equation, correct to order v/c, is used to derive a flux limiter valid in high-velocity hydrodynamic flows. In the limit v = 0 the widely used result of Levermore and Pomraning (LP) (1982) is recovered. In the case of homologous flow (v varies as R) the LP result remains valid, but in the presence of shock waves and other nonhomologous flows differences may be large. We calculate the Eddington factors, which are significantly altered, and discuss the importance of having them possess the correct form in the presence of a shock wave, e.g., on the neutrino transport during the formation of a supernova.

Cooperstein, J.↗

Theoretical rocket performance of JP-4 fuel with mixtures of liquid ozone and fluorine

Data were estimated by means of a heat correction equation using data for JP-4 fuel with mixtures of oxygen and flourine. The estimated data were checked for several cases by direct calculations. The difference in specific impulse between the estimated and directly calculated values was from 0.2 to 0.8 pound-second per pound. The maximum value of specific impulse was 334.9 pound-seconds per pound for a combustion-chamber pressure of 600 pounds per square inch absolute and an exit pressure of 1 atmosphere.

Huff, Vearl N↗

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗

Simulation of Acoustic Scattering from a Trailing Edge

Three model problems were examined to assess the difficulties involved in using a hybrid scheme coupling flow computation with the the Ffowcs Williams and Hawkings equation to predict noise generated by vortices passing over a sharp edge. The results indicate that the Ffowcs Williams and Hawkings equation correctly propagates the acoustic signals when provided with accurate flow information on the integration surface. The most difficult of the model problems investigated inviscid flow over a two-dimensional thin NACA airfoil with a blunt-body vortex generator positioned at 98 percent chord. Vortices rolled up downstream of the blunt body. The shed vortices possessed similarities to large coherent eddies in boundary layers. They interacted and occasionally paired as they convected past the sharp trailing edge of the airfoil. The calculations showed acoustic waves emanating from the airfoil trailing edge. Acoustic directivity and Mach number scaling are shown.

Singer, Bart A.↗

Cerium Stable Isotope Analysis of Synthetic and Terrestrial Rock Reference Materials by MC-ICPMS

Cerium is the most abundant rare earth element (REE) in the solar photosphere, CI chondrites, and the Earth. It has four main stable isotopes (masses: 136,138,140, and 142), with 138Ce being the most studied species, used in geochronology and petrogenesis. In addition, more abundant 140Ce and 142Ce are suggested to be potentially applicable in geochemical investigations. In this work, we developed a modified four-step ion chromatography procedure for Ce chemical separation. Using a MC-ICPMS, we designed a cup configuration to measure 142Ce/140Ce ratio of the samples with an optimized Nd correction equation. A 0.03‰ (2SD) reproducibility was obtained for Ce Ames metal standard. We analyzed ten different igneous and one sedimentary geochemical reference materials. Mean δ142Ce range from −0.07 to 0.32‰. Most of the samples show a heavier Ce isotopic composition than the Ce Ames standard. The majority of rocks have a homogenous δ142Ce. The δ142Ce does not show any correlation with rock chemical composition including their Ce content or rock types. A carbonatite (SARM 40) has a mean δ142Ce of −0.07 ± 0.13‰ (2SD), lower than the other rocks, suggesting the possibility of a pronounced isotopic fractionation. Our work demonstrates the applicability of the developed methodology and the potential of Ce stable isotopes for future geochemical studies. Production of a larger database of δ142Ce values is required to obtain a clearer view on the similarities and differences between different geological material and explaining Ce stable isotope dynamics.

Cerium↗

Correction function in the Lidar equation and the solution techniques for CO2 Lidar date reduction

For lidar systems with long laser pulses the unusual behavior of the near-range signals causes serious difficulties and large errors in reduction. The commonly used lidar equation is no longer applicable since the convolution of the laser pulse with the atmospheric parameter distributions should be taken into account. It is important to give more insight into this problem and find the solution techniques. Starting from the original equation, a general form is suggested for the single scattering lidar equation where a correction function Cr is introduced. The correction Function Cr(R) derived from the original equation indicates the departure from the normal lidar equation. Examples of Cr(R) for a coaxial CO2 lidar system are presented. The Differential Absorption Lidar (DIAL) errors caused by the differences of Cr(R) for H2O measurements are plotted against height.

Zhao, Y.↗

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Thomas, J. L.↗

Two-dimensional transonic wind-tunnel wall interference corrections based on the Euler equations

A procedure for the evaluation of wall interference corrections for two-dimensional models is presented. The Mach number and angle-of-attack corrections require the numerical solution of the Euler equations. Pressure measurements are required near the wind tunnel walls. The correction procedure also requires knowledge of the free-stream Mach number, the model geometry, and the lift force experienced by the model. The residual interference not accounted for by the Mach number and angle-of-attack corrections is estimated.

Rizk, M. H.↗

Reanalysis procedure for large structural systems

Global-basis-vector approximate reanalysis techniques for use in automated structural optimization schemes are developed and demonstrated. The vibrational response of a modified structure (MS) is estimated by lumping the design variables into a single tracing parameter, applying an operator splitting procedure to express the FEM equations of the MS in terms of the original-structure equations plus correction terms, and reducing the MS equations via a classical Bubnov-Galerkin scheme. The sensitivity of the vibrational response to structural modifications is evaluated, and the relationship between this method and the preconditioned conjugate-gradient method (Noor and Peters, 1988) is explored. Numerical results for linear static and free vibration problems involving beamlike lattices, double-layered hexahedral grids, and structural gridworks are presented in tables and graphs and briefly characterized.

Noor, Ahmed K.↗

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗

Integral equation formulation for probe corrected far-field reconstruction from measurements on a cylinder

A method has been developed for far-field evaluation from measurements taken on a cylinder. The antenna and probe fields are represented by superpositions of plane waves, and two integral equations are derived whose functions are the elevation and azimuthal components of the antenna pattern. The known components are the measurements taken by either two probes or a single probe with two geometrical orientations. The convolutional nature of the integral equations makes Fourier analysis techniques applicable to a straightforward solution and an efficient computational procedure. Good agreement has been found between experimental and reconstructed patterns for both nominal and cross polarized field components.

Borgiotti, G. V.↗

Comparison of experiment with calculations using curvature-corrected zero and two equation turbulence models for a two-dimensional U-duct

In this paper experimental measurements are compared with Navier-Stokes calculations using seven different turbulence models for the internal flow in a two-dimensional U-duct. The configuration is representative of many internal flows of engineering interst that experience strong curvature. In an effort to improve agreement, this paper tests several versions of the two-equation k-epsilon turbulence model including the standard version, an extended version with a production range time scale, and a version that includes curvature time scales. Each is tested in its high and low Reynolds number formulations. Calculations using these new models and the original mixing length model are compared here with measurements of mean and turbulence velocities, static pressure and skin friction in the U-duct at two Reynolds numbers. The comparisons show that only the low Reynolds number version of the extended k-epsilon model does a reasonable job of predicting the important features of this flow at both Reynolds numbers tested.

Monson, D. J.↗

Modified Hitschfeld-Bordan Equations for Attenuation-Corrected Radar Rain Reflectivity: Application to Nonuniform Beamfilling at Off-Nadir Incidence

As shown by Takahashi et al., multiple path attenuation estimates over the field of view of an airborne or spaceborne weather radar are feasible for off-nadir incidence angles. This follows from the fact that the surface reference technique, which provides path attenuation estimates, can be applied to each radar range gate that intersects the surface. This study builds on this result by showing that three of the modified Hitschfeld-Bordan estimates for the attenuation-corrected radar reflectivity factor can be generalized to the case where multiple path attenuation estimates are available, thereby providing a correction to the effects of nonuniform beamfilling. A simple simulation is presented showing some strengths and weaknesses of the approach.

nonuniform beamfilling↗

Correction of Temperatures of Air-Cooled Engine Cylinders for Variation in Engine and Cooling Conditions

Factors are obtained from semiempirical equations for correcting engine-cylinder temperatures for variation in important engine and cooling conditions. The variation of engine temperatures with atmospheric temperature is treated in detail, and correction factors are obtained for various flight and test conditions, such as climb at constant indicated air speed, level flight, ground running, take-off, constant speed of cooling air, and constant mass flow of cooling air. Seven conventional air-cooled engine cylinders enclosed in jackets and cooled by a blower were tested to determine the effect of cooling-air temperature and carburetor-air temperature on cylinder temperatures. The cooling air temperature was varied from approximately 80 degrees F. to 230 degrees F. and the carburetor-air temperature from approximately 40 degrees F. to 160 degrees F. Tests were made over a large range of engine speeds, brake mean effective pressures, and pressure drops across the cylinder. The correction factors obtained experimentally are compared with those obtained from the semiempirical equations and a fair agreement is noted.

Schey, Oscar W↗

Effect of the cluster integrals on three particles on the calculated electron density of a hydrogen plasma

The effect of the calculation of the cluster integrals on three particles is analyzed and evaluated for a hydrogen plasma where a pairwise-additive hard sphere-Coulomb potential is assumed. The Mayer cluster integral method was used to calculate the Helmholtz free energy which was then applied to the calculation of the electron number density through an iterative technique using a corrected Saha equation. It is seen that the three particle integrals provide a substantial correction to the calculations in the low energy-high density region of the hydrogen plasma.

Mcintyre, R. G.↗

Thermal shaft effects on load-carrying capacity of a fully coupled, variable-properties cryogenic journal bearing

The purpose of this work was to perform a rather complete analysis for a cryogenic (oxygen) journal bearing. The Reynolds equation required coupling and simultaneous solution with the fluid energy equation. To correctly account for the changes in the fluid viscosity, the fluid energy equation was coupled with the shaft and bearing heat conduction energy equations. The effects of pressure and temperature on the density, viscosity, and load-carrying capacity were further discussed as analysis parameters, with respect to relative eccentricity and the angular velocity. The isothermal fluid case and the adiabatic fluid case represented the limiting boundaries. The discussion was further extrapolated to study the Sommerfeld number dependency on the fluid Nusselt number and its consequence on possible total loss of load-carrying capacity and/or seizure (catastrophic failure).

Braun, M. J.↗

Structure of Weak Shock Waves in a Monatomic Gas

The profiles and thicknesses of normal shock waves in argon at Mach numbers of 1.335, 1.454, 1.576, and 1-713 were determined experimentally by means of a free-molecule probe whose equilibrium temperature is related by kinetic theory to the local flow properties and their gradients. Comparisons were made between the experimental shock profiles and the theoretical profiles calculated from the Navier-Stokes equations, the Grad 13-moment equations, and the Burnett equations. New, very accurate numerical integrations of the Burnett equations were obtained for this purpose with results quite different from those found by Zoller, to whom the solution of this problem is frequently attributed. The experimental shock profiles were predicted with approximately equal success by the Navier-Stokes and Burnett theories, while the 13-moment method was definitely less satisfactory. A surprising feature of the theoretical results is the relatively small difference in predictions between the Navier-Stokes and Burnett theories in the present range of shock strengths and the contrastingly large difference between predictions of Burnett and the 13-moment theories. It is concluded that the Navier-Stokes equations are correct for weak shocks and that within the present shock strength range the Burnett equations make no improvement which merits the trouble of solving them. For shocks of noticeably greater strength, say with a shock Mach number of more than 2.5, it remains fundamentally doubtful that any of these theories can be correct.

Sherman, F. S.↗