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NASA NTRSDate not supplied

Evaluation of Heat Transfer Coefficient from Velocity Distribution in Boundary Layer

This paper describes a method of evaluating heat transfer coefficient from a velocity distribution in the boundary layer. The power law velocity profile and universal velocity distribution in a smooth pipe have been used to evaluate the wall shear stress, and the heat transfer coefficient was evaluated from the wall shear stress using the Chilton-Colburn analogy. The predicted pressure drop was compared with the pressure drop computed by the Colebrook equation, and the predicted heat transfer coefficient was compared with the heat transfer coefficient calculated by the Dittus-Boelter equation. The accuracy of pressure drop prediction was within 1%, and the accuracy of heat transfer coefficient prediction was within 8%. This method has the potential to use a Navier-Stokes based CFD solution to evaluate the heat transfer coefficient in nodal or network flow codes.

Heat Transfer Coefficient↗
DOE OSTI2025

Applying a Compact Porous Media Model to Numerically Derive Resistance Coefficients for Lattice Structures

Additive Manufacturing allows for exploring various geometries to achieve specific engineering criteria. Lattices are one geometry with unique properties, including being periodically repeating structures which allow flow through them to be represented as a porous media according to Darcy-Forchheimer equations. These equation’s coefficients are generally experimentally derived, but this work demonstrates the ability to numerically derive them with CFD. Simulations were performed using three-dimensional stead state Reynolds-averaged Navier-Stokes with a k-ω Shear Stress Transport turbulence model using Ansys Fluent. Three lattice geometries were investigated and drag coefficients were derived. The method was validated against externally published data for similar geometries demonstrating strong agreement, and grid convergence for all simulations was calculated with a Grid Convergence Index method. Wall roughness is demonstrated to have a non-negligible impact on results and roughness values are considered for the primary focus Octahedral geometry where both smooth wall and rough wall coefficients were derived. The porosity coefficients for the Octahedral geometry at 1.0 [m/s] were found to be 2.89×10 6 and 2.90×10 6 [1/(Pa*m*s)] for the permeability coefficients, 6.37×10 1 and 5.44×10 1 [m 2 /kg] for the inertial resistance coefficients, and with a max pressure drop of 5116.7 [Pa] and 4429.5 [Pa] for the smooth walls and rough walls, respectively. The derived numerical method enables rapid exploration and optimization of new lattice designs for diverse engineering applications.

42 ENGINEERING↗
DOE OSTI2026

Molecular dynamics simulation of hydrodynamic transport coefficients in plasmas

Molecular dynamics simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity are computed using the Green–Kubo formalism over a broad range of Coulomb coupling strength, 0.01 ≤ Γ ≤ 140. Emphasis is placed on testing standard results of the Chapman–Enskog solution in the weakly coupled regime (Γ ≪ 1) using these first-principles simulations. As expected, the results show good agreement for Γ ≲ 0.1. However, this agreement is only possible if careful attention is paid to the definitions of linear constitutive relations in each of the theoretical models, a point that is often overlooked. For example, the standard Green–Kubo expression for thermal conductivity is a linear combination of thermal conductivity, electrothermal, and thermoelectric coefficients computed in the Chapman–Enskog formalism. Meaningful results for electrical conductivity are obtained over the full range of coupling strengths explored, but it is shown that potential and virial components of the other transport coefficients diverge in the strongly coupled regime (Γ ≫ 1). In this regime, only the kinetic components of the transport coefficients are meaningful for a classical plasma.

Electrical conductivity↗
DOE OSTI2024

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction↗
NASA NTRS1973

Directional diffusion coefficients of solar protons inside and outside the bow shock.

The directional diffusion coefficients of low-energy (greater than or equal to 0.3 MeV) solar protons inside and outside the bow shock are examined during the solar flare event of Jan. 24, 1969. The data are derived from simultaneous observations obtained by Explorer 33 inside the magnetosheath and by Explorer 35 in the interplanetary medium. Although the gross properties of the spin-averaged intensities on a diffusion-type plot appear to be the same in both media, the directional intensities show significant variations. It is shown that directional intensities of low-energy protons can be described reasonably well by anisotropic diffusion with an associated diffusion coefficient. Directional diffusion coefficients are found to differ by a factor of as much as three among different directions in space, and from the spin-averaged diffusion coefficient. This suggests that anisotropic diffusion does indeed take place and that so called 'isotropic' diffusion coefficients derived in the past from spin-averaged intensities may actually be directional diffusion coefficients in cases where substantial anisotropies (greater than 50%) exist.

Verzariu, P.↗
NASA NTRS1980

The SASS scattering coefficient algorithm

This paper describes the algorithms used to convert engineering unit data obtained from the Seasat-A satellite scatterometer (SASS) to radar scattering coefficients and associated supporting parameters. A description is given of the instrument receiver and related processing used by the scatterometer to measure signal power backscattered from the earth's surface. The applicable radar equation used for determining scattering coefficient is derived. Sample results of SASS data processed through current algorithm development facility (ADF) scattering coefficient algorithms are presented which include scattering coefficient values for both water and land surfaces. Scattering coefficient signatures for these two surface types are seen to have distinctly different characteristics. Scattering coefficient measurements of the Amazon rain forest indicate the usefulness of this type of data as a stable calibration reference target.

Bracalente, E. M.↗
NASA NTRS1984

Partition coefficients of Hf, Zr, and REE between phenocrysts and groundmasses

Partition coefficients of Hf, Zr, and REE between olivine, orthopyroxene, clinopyroxene, plagioclase, garnet, amphibole, ilmenite, phlogopite, and liquid are presented. Samples consist of megacrysts in kimberlite, phenocrysts in alkaline basalts, tholeiitic basalts and andesitic to dacitic rocks, and synthetic garnet and clinopyroxene in Hawaiian tholeiites. The Hf-Lu and Zr-Lu elemental fractionations are as large as the Lu-Sm or Lu-Nd fractionation. The Hf and Zr partition coefficients between mafic phenocrysts and liquids are smaller than the Lu partition coefficients, but are similar to the Nd or Sm partition coefficients. The Hf and Zr partition coefficients between ilmenite, phlogopite, and liquid are larger than the Lu partition coefficients for these minerals and their corresponding liquids. The Hf-Zr elemental fractionation does not occur except for extreme fractionation involving Zr-minerals and extremely low fO2. These data have an important bearing on chronological and petrogenetic tracer studies involving the Lu-Hf isotopic system.

Fujimaki, H.↗
NASA NTRS1984

Measurement and analysis of distribution coefficients in Fe-Ni alloys containing S and/or P. I - K sub Ni and K sub P

The distribution coefficients of Ni and P in Fe-Ni-S-P alloys are determined using a plane front solidification technique. It is found that the distribution coefficient of Ni is altered only when both S and P are present as alloy constituents; the coefficient increases with S and P contents in the liquid alloy and varies from 0.9 to 1.30. The behavior of the distribution coefficient of P is determined by the S/P ratio in the liquid; the coefficient increases with the S/P ratio and varies from 0.25 to 5.8. Expressions are presented which relate the distribution coefficients of Ni and P to the S and P contents in the liquid.

Sellamuthu, R.↗
NASA NTRS1987

An experimental and theoretical comparison of rotordynamic coefficients for sawtooth-pattern damper seals

A brief review of the annular seal theory as related to rotordynamics for liquid seals is presented. Also included is an overview of Childs and Kim's current theory for calculating empirical turbulence coefficients and predicting stiffness and damping coefficients for surface roughened damper seals. The designation sawtooth-pattern refers to a seal stator with a roughness pattern whose cross section normal to the seal axis resembles a sawtooth with the teeth directed against the flow. The net stiffness and damping coefficients for the eleven seals are compared to each other, a smooth seal, and the optimum-configuration damper seal previously tested. The experimental force coefficients, the net damping, and the net stiffness coefficients for four of the sawtooth seals are compared to the predictions of Childs and Kim's analysis. The sawtooth-pattern seal had less net damping than the hole-pattern seal but more than the smooth seal. The stiffness was comparable to the hole-pattern. Both the sawtooth and hole-pattern seals leaked less than the smooth seal, while the sawtooth-pattern seal with maximum damping leaked more than the hole-pattern seal. The theoretical predictions compared relatively poorly to the experimental results obtained for the rotordynamic coefficients of the seals investigation.

Nolan, Steven Anthony↗
NASA NTRS1993

New limb-darkening coefficients for modeling binary star light curves

We present monochromatic, passband-specific, and bolometric limb-darkening coefficients for a linear as well as nonlinear logarithmic and square root limb-darkening laws. These coefficients, including the bolometric ones, are needed when modeling binary star light curves with the latest version of the Wilson-Devinney light curve progam. We base our calculations on the most recent ATLAS stellar atmosphere models for solar chemical composition stars with a wide range of effective temperatures and surface gravitites. We examine how well various limb-darkening approximations represent the variation of the emerging specific intensity across a stellar surface as computed according to the model. For binary star light curve modeling purposes, we propose the use of a logarithmic or a square root law. We design our tables in such a manner that the relative quality of either law with respect to another can be easily compared. Since the computation of bolometric limb-darkening coefficients first requires monochromatic coefficients, we also offer tables of these coefficients (at 1221 wavelength values between 9.09 nm and 160 micrometer) and tables of passband-specific coefficients for commonly used photometric filters.

Van Hamme, W.↗
NASA NTRS1998

Self-Broadening and Self-Shift Coefficients in the Fundamental Band of 12C 16O

High quality and precise measurements of self-broadened and self-shift coefficients in the fundamental band of C-12O-16 were made using spectra recorded at room temperature with the high-resolution (0.0027 cm(exp -1)) McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak, Arizona. The spectral region under investigation (2008-2247 cm(exp -1)) contains the P(31) to R(31) transitions. The data were obtained using a high-purity natural isotopic sample ofcarbon monoxide and two absorption cells with pathlengths of 4.08 and 9.98 cm, respectively. Various pressures of CO were used, ranging between 0.25 and 201.2 Torr. The results were obtained by analyzing five spectra simultaneously, using a multispectrum nonlinear least-squares fitting technique. The self-broadened coefficients ranged from 0.0426(2) cm(exp -1) atm(exp -1) at 296 K to 0.0924(2) cm(exp -1) atm(exp -1) at 296 K, while the pressure-induced shift coefficients varied between -0.0042(3) cm(exp -1) atm(exp -1) at 296 K and +0.0005(l) cm(exp -1) atm(exp -1) at 296 K. The value in parentheses is the estimated uncertainty in units of the last digit. The self-broadened coefficients of lines with same values of m in the P and R branches agree close to within experimental uncertainties while the self-shift coefficients showed considerable variation within and between the two branches. The mean value of the ratios of P branch to R branch self-broadened coefficients was found to be 1.01 with a standard deviation of + or - 0.01. Comparisons of the results with other published data were made.

Devi, Malathy V.↗
NASA NTRS2006

Derivation of Improved Surface and TOA Broadband Fluxes Using CERES-derived Narrowband-to-Broadband Coefficients

Satellites can provide global coverage of a number of climatically important radiative parameters, including broadband (BB) shortwave (SW) and longwave (LW) fluxes at the top of the atmosphere (TOA) and surface. These parameters can be estimated from narrowband (NB) Geostationary Operational Environmental Satellite (GOES) data, but their accuracy is highly dependent on the validity of the narrowband-to-broadband (NB-BB) conversion formulas that are used to convert the NB fluxes to broadband values. The formula coefficients have historically been derived by regressing matched polarorbiting satellite BB fluxes or radiances with their NB counterparts from GOES (e.g., Minnis et al., 1984). More recently, the coefficients have been based on matched Earth Radiation Budget Experiment (ERBE) and GOES-6 data (Minnis and Smith, 1998). The Clouds and the Earth's Radiant Energy Budget (CERES see Wielicki et al. 1998)) project has recently developed much improved Angular Distribution Models (ADM; Loeb et al., 2003) and has higher resolution data compared to ERBE. A limited set of coefficients was also derived from matched GOES-8 and CERES data taken on Topical Rainfall Measuring Mission (TRMM) satellite (Chakrapani et al., 2003; Doelling et al., 2003). The NB-BB coefficients derived from CERES and the GOES suite should yield more accurate BB fluxes than from ERBE, but are limited spatially and seasonally. With CERES data taken from Terra and Aqua, it is now possible to derive more reliable NB-BB coefficients for any given area. Better TOA fluxes should translate to improved surface radiation fluxes derived using various algorithms. As part of an ongoing effort to provide accurate BB flux estimates for the Atmospheric Radiation Measurement (ARM) Program, this paper documents the derivation of new NB-BB coefficients for the ARM Southern Great Plains (SGP) domain and for the Darwin region of the Tropical Western Pacific (DTWP) domain.

Khaiyer, Mandana M.↗
NASA NTRS2011

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Lei, Ning↗
NASA NTRS2017

Atmospheric Form Drag Coefficients Over Arctic Sea Ice Using Remotely Sensed Ice Topography Data, Spring 2009-2015

Sea ice topography significantly impacts turbulent energy/momentum exchange, e.g., atmospheric (wind) drag, over Arctic sea ice. Unfortunately, observational estimates of this contribution to atmospheric drag variability are spatially and temporally limited. Here we present new estimates of the neutral atmospheric form drag coefficient over Arctic sea ice in early spring, using high-resolution Airborne Topographic Mapper elevation data from NASA's Operation IceBridge mission. We utilize a new three-dimensional ice topography data set and combine this with an existing parameterization scheme linking surface feature height and spacing to form drag. To be consistent with previous studies investigating form drag, we compare these results with those produced using a new linear profiling topography data set. The form drag coefficient from surface feature variability shows lower values [less than 0.5-1 × 10(exp. −3)] in the Beaufort/Chukchi Seas, compared with higher values [greater than 0.5-1 ×10(exp. −3)] in the more deformed ice regimes of the Central Arctic (north of Greenland and the Canadian Archipelago), which increase with coastline proximity. The results show moderate interannual variability, including a strong increase in the form drag coefficient from 2013 to 2014/2015 north of the Canadian Archipelago. The form drag coefficient estimates are extrapolated across the Arctic with Advanced Scatterometer satellite radar backscatter data, further highlighting the regional/interannual drag coefficient variability. Finally, we combine the results with existing parameterizations of form drag from floe edges (a function of ice concentration) and skin drag to produce, to our knowledge, the first pan-Arctic estimates of the total neutral atmospheric drag coefficient (in early spring) from 2009 to 2015.

sea ice↗
NASA NTRS2016

Comparison of Quantum Mechanical and Empirical Potential Energy Surfaces and Computed Rate Coefficients for N2 Dissociation

Physics-based modeling of hypersonic flows is predicated on the availability of chemical reaction rate coefficients and cross sections for the collisional processes. This approach has been built around the use of quantum mechanical calculations to describe the interaction between the colliding particles. In this approach a potential energy surface (PES) is computed by solving the electronic Schrödinger equation and collision cross sections are determined for that PES using classical, semiclassical or quantum mechanical scattering methods. The rate coefficients are computed by integrating the thermally weighted cross sections. State-to-state rate coefficients are determined by only integrating over a thermal distribution of collisional energies. Finally, thermal rate coefficients are determined by summation of the state-to-state rate coefficients for reactions of molecules in all relevant ro-vibrational energy levels. If the flow is in thermal non-equilibrium, the translational, vibrational and rotational energy modes can be represented in different ways: three unique temperatures can be used to describe the distributions, the populations of individual ro-vibrational energy levels can be determined by solving the Master Equation, or through the use of direct simulation in particle-based Monte Carlo sampling. The PES-to-rate coefficient approach had been proposed and attempted in the early days of digital computing, but it is only in the last 15 years that computer hardware and software have been up to the task of calculating accurate interatomic and intermolecular potentials.

Jaffe, Richard L.↗
NASA NTRSDate not supplied

The UV Aerosol Extinction Coefficients Retrieval Using the Ground-Based Ozone Lidar

NASA Langley Mobile Ozone Lidar (LMOL) has capability to measure the O3 concentration from 0.1 to 8 km. A new method is proposed to retrieve the aerosol backscatter and extinction coefficients from the LMOL attenuated backscatter signals. The LMOL attenuated backscatter data are corrected by the O3 concentration determined by LMOL system. The aerosol extinction coefficients are retrieved by using Fernald-type method. The retrieved aerosol extinction coefficient profiles are compared with the coincident aerosol extinction coefficient profiles provided by overflights of the airborne High Altitude Lidar Observatory (HALO) system during the 2018 LISTOS campaign. Results show the new method has the capability to retrieve aerosol extinction coefficients from 0.1-8 km at night and 0.1-4 km during the day for 5 minute temporal averaging. The profile time series of the retrieved aerosol extinction coefficient are also compared with co-located ceilometer data, showing general agreement with aerosol features and dynamics. The impact of lidar extinction to backscatter ratios on the retrievals is also presented.This new method extends LMOL’s ability to quantitatively determine the vertical distribution of aerosol optical properties. This is expected to contribute to further understanding of the relationship between the ozone and aerosol in the wildfire emissions transport and impact on local air quality during the LISTOS campaign.

Liqiao Lei↗
NASA NTRSDate not supplied

Experimental Calibration of Flow Rule Coefficients for LS-Dyna Mat_213

Composite materials have become a popular choice in aerospace engineering applications due to their low weight, high specific stiffness, high specific energy absorption, and economic synthesis. As use of composite materials has proliferated, the need for accurate simulation under extreme loading conditions is of increasing importance. *MAT_213 is a tabulated plasticity and damage material model in LS-DYNA designed for such use cases. To account for the nonlinear material response, a plasticity algorithm is used, which employs a non-associative flow rule with coefficients requiring experimental calibration. This work outlines an experimental methodology for calibrating these coefficients using the macroscopic stress-strain response and microscopic in-plane strain measurements from coupon scale experiments. The model material used for the development and demonstration of this methodology is a plain weave woven fabric with T300 carbon fiber tows in the warp direction and Kevlar© 49 fiber tows in the weft direction, and an Epon© 828/Epikure© 3223 thermoset epoxy matrix. Coupon-scale tensile testing performed at multiple fiber angles (carbon fibers oriented 0º, 22.5º, 45º, 67.5º, and 90º relative to the loading axis) provides data for multiple calibration processes. The measured plastic strain increments in the principal material coordinate are used to set limits for ratios between flow rule coefficients. The identified ranges are used to bound the search for a set of coefficients, leading to convergence of different coupon responses in the effective stress – effective plastic strain space. Flow rule coefficients found by this methodology are then used as (i) input for LS-DYNA simulations of uniaxial tension coupon tests at varying fiber angles, and (ii) comparison of predicted values for the plastic Poisson’s ratio in global coordinates with the experimentally measured one for all off-axis orientations. These results are quantitatively and qualitatively compared to macroscopic stress-strain curves and experimental strain components. The conformity of the experimentally measured quantities with those derived from the simulations provide a means for assessing the quality of calibrated coefficients.

Polymer Matrix Composites↗
NASA NTRS2016

Comparison of Quantum Mechanical and Empirical Potential Energy Surfaces and Computed Rate Coefficients for N2 Dissociation

Comparisons are made between potential energy surfaces (PES) for N2 + N and N2 + N2 collisions and between rate coefficients for N2 dissociation that were computed using the quasiclassical trajectory method (QCT) on these PESs. For N2 + N we compare the Laganas empirical LEPS surface with one from NASA Ames Research Center based on ab initio quantum chemistry calculations. For N2 + N2 we compare two ab initio PESs (from NASA Ames and from the University of Minnesota). These use different methods for computing the ground state electronic energy for N4, but give similar results. Thermal N2 dissociation rate coefficients, for the 10,000K-30,000K temperature range, have been computed using each PES and the results are in excellent agreement. Quasi-stationary state (QSS) rate coefficients using both PESs have been computed at these temperatures using the Direct Molecular Simulation of Schwartentruber and coworkers. The QSS rate coefficients are up to a factor of 5 lower than the thermal ones and the thermal and QSS values bracket the results of shock-tube experiments. We conclude that the combination of ab initio quantum chemistry PESs and QCT calculations provides an attractive approach for the determination of accurate high-temperature rate coefficients for use in aerothermodynamics modeling.

quasiclassical trajectory method↗