SEARCH · Engineering Papers
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.
New method of computation of gravitational field of Earth provides for conversion of gravity-bin parameters to coefficients of spherical harmonics. Traditional representation of gravitational field recovered by new method.
A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.
We study the use of P{sub N} method in angle and discontinuous Galerkin is space to solve 3D neutron transport problem. P{sub N} method consists in developing the angular flux on truncated spherical harmonics basic. In this paper, we couple this method with the discontinuous finite elements in space to obtain a complete discretization of the multigroup neutron transport equation. To investigate its precision, the method was applied to Takeda and C5G7 benchmark problems. These calculations point out that the proposed P{sub N}-DG method is capable of producing accurate solutions in small computational time, and that it is able to handle complex 3D geometries. (authors)
The direct method for the solution of the spherical harmonics approximation to the equation of transfer of radiation is applied to the cases of (1) scattering of the solar radiation in the atmosphere with the Lambertian boundary and (2) thermal radiation transfer.
In this study, interaction force of non-spherical particles in low Reynolds number gas-solid flow is investigated by neural network approaches. An artificial neural network (ANN) model is developed to correlate the non-spherical particle shape and the flow conditions with the interaction force. To define the particle shape, spherical harmonic expansion is applied. Furthermore, variational autoencoder model is then used to extract latent geometric features. The latent vector is utilized as an input with the Reynolds number for the ANN. The interaction force data, which is used as output data of the ANN, is obtained by particle resolved direct numerical simulation for 5200 non-spherical particles. The proposed model enables unsupervised extraction for non-spherical particle shapes and accurate predictions on the interaction force without heavy computation. This study provides the model that can explain complicated shapes of particles and be applied to a large scale, computational fluid dynamics simulation.
Radiative transfer/radiation transport are important problems to solve in astrophysics and high energy density physics. Various methods exist to solve radiation transport, such as Monte Carlo (MC), Discrete Ordinates (S N ), Method of Characteristics (MOC), and the spherical harmonics (P N ) method. Method of Characteristics requires “launching” of rays in discrete directions. Unresolved details of angular mesh create ray effects and can miss sources in the domain. Ray effects can lead to unphysical “stepping” in solution and incorrect energy deposition. Adaptive quadrature schemes can be used to detect and mitigate these effects. The Method of Characteristics (MOC) is a common method for solving hyperbolic PDEs in radiation transport and supersonic flow problems. Generally in MOC for radiation transport, virtual particles are tracked from birth to the end of a timestep. This requires interpolation to go from final location to cell averaged or corner values of angular intensity. Backwards-in-Time (BIT) particle tracking avoids this by prescribing the final position of the virtual particle at the cell nodes/corners. Angular intensities are computed at time k + 1 by launching ray back to previous timestep(s), or t = 0. Scheme allows solution to be computed as the characteristic ray is traced backwards in time.
The computer-assisted C-matrix, Loewdin-alpha-function, single-center expansion method in spherical harmonics has been applied to the three-center nuclear-attraction integral (potential due to the product of separated Slater-type orbitals). Exact formulas are produced for 13 terms of an infinite series that permits evaluation to ten decimal digits of an example using 1s orbitals.
We report results from searches for anisotropic stochastic gravitational-wave backgrounds using data from the first three observing runs of the Advanced LIGO and Advanced Virgo detectors. For the first time, we include Virgo data in our analysis and run our search with a new efficient pipeline called PyStochon data folded over one sidereal day. We use gravitational-wave radiometry(broadband and narrow band) to produce sky maps of stochastic gravitational-wave backgrounds and to search for gravitational waves from point sources. A spherical harmonic decomposition method is employed to look for gravitational-wave emission from spatially-extended sources. Neither technique found evidence of gravitational-wave signals. Hence we derive 95% confidence-level upper limit sky maps on the gravitational-wave energy flux from broadband point sources, ranging from F(α,Θ) < (0.013−7.6)×10^(−8)erg/sq. cm s Hz,and on the (normalized) gravitational-wave energy density spectrum from extended sources, ranging from Ω(α,Θ) < (0.57−9.3)×10^(−9) per sr, depending on direction (Θ) and spectral index (α). These limits improve upon previous limits by factors of 2.9−3.5. We also set 95% confidence level upper limits on the frequency-dependent strain amplitudes of quasimonochromatic gravitational waves coming from three interesting targets, Scorpius X-1, SN1987A and the Galactic Center, with best upper limits range fromh(0) < (1.7−2.1)×10^(−25), a factor of ≥ 2.0 improvement compared to previous stochastic radiometer searches.
Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.
The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.
Fluid motions in the electrically conducting core and magnetized crustal rocks are the two major sources of the magnetic field observed on or slightly above the Earth's surface. The exact separation of these two contributions is not possible without imposing a priori assumptions about the internal source distribution. Nonetheless models like these were developed for hundreds of years Gauss' method, least squares analysis with a truncated spherical harmonic expansion was the method of choice for more than 100 years although he did not address separation of core and crustal sources, but rather internal versus external ones. Using some arbitrary criterion for appropriate truncation level, we now extrapolate downward core field models through the (approximately) insulating mantle. Unfortunately our view can change dramatically depending on the degree of truncation for describing core sources.
This project, supported by the NASA New Investigator Program, has primarily been funding a graduate student, Darren McKague. Since August 1999 Darren has been working part time at Raytheon, while continuing his PhD research. Darren is planning to finish his thesis work in May 2001, thus some of the work described here is ongoing. The proposed research was to use GOES visible and infrared imager data and SSM/I microwave data to obtain joint distributions of cirrus cloud ice mass and precipitation for a study region in the Eastern Tropical Pacific. These joint distributions of cirrus cloud and rainfall were to be compared to those from the CSU general circulation model to evaluate the cloud microphysical amd cumulus parameterizations in the GCM. Existing algorithms were to be used for the retrieval of cloud ice water path from GOES (Minnis) and rainfall from SSM/I (Wilheit). A theoretical study using radiative transfer models and realistic variations in cloud and precipitation profiles was to be used to estimate the retrieval errors. Due to the unavailability of the GOES satellite cloud retrieval algorithm from Dr. Minnis (a co-PI), there was a change in the approach and emphasis of the project. The new approach was to develop a completely new type of remote sensing algorithm - one to directly retrieve joint probability density functions (pdf's) of cloud properties from multi-dimensional histograms of satellite radiances. The usual approach is to retrieve individual pixels of variables (i.e. cloud optical depth), and then aggregate the information. Only statistical information is actually needed, however, and so a more direct method is desirable. We developed forward radiative transfer models for the SSM/I and GOES channels, originally for testing the retrieval algorithms. The visible and near infrared ice scattering information is obtained from geometric ray tracing of fractal ice crystals (Andreas Macke), while the mid-infrared and microwave scattering is computed with Mie scattering. The radiative transfer is performed with the Spherical Harmonic Discrete Ordinate Method (developed by the PI), and infrared molecular absorption is included with the correlated k-distribution method. The SHDOM radiances have been validated by comparison to version 2 of DISORT (the community "standard" discrete-ordinates radiative transfer model), however we use SHDOM since it is computationally more efficient.
Inversion of magnetic data from the MAGSAT satellite, to arrive at intensities of magnetization of the Earth's crust, was performed by two different methods. The first method uses a spherical harmonic model of the magnetic field. The coefficients believed to represent sources in the Earth's crust can then be inverted to arrive at vertical dipole moments per unit area at the Earth's surface. The spherical harmonic models contain coefficients of degrees of harmonics up to 23. The dipole moment per unit area for a surface element can then be determined by summing the contribution for each individual degree of harmonic. The magnetic moments were calculated for continental and oceanic areas separately as well as over certain latitudinal segments. Of primary concern was to determine whether there are any differences between continental and oceanic areas. The second analysis with magnetization intensities was made using narrower ranges of degrees of harmonics, assuming that higher degrees are present in the core field signal.
Current and future earth observation programs depend on satellite measurements of radiance to retrieve the properties of clouds on a global basis. At present, this retrieval is made assuming that the clouds in the instrument field of view are plane parallel and independent of adjacent pixels. While this assumption is known to be false except in very limited cases, its impact can be evaluated, and if possible corrected, based on emerging theoretical techniques. In this study, the Spherical Harmonic Discrete Ordinate Method (SHDOM, Evans, 1996) has been used to assess the sensitivity of the retrieval to a variety of cloud parameters. SHDOM allows the plane parallel assumption to be relaxed and makes 2D and even 3D radiative solutions practical. A previous study (Chambers et al., 1996) assessed the effect of horizontal inhomogeneity in 45 LANDSAT scenes of boundary layer clouds over ocean. The four scenes studied here represent overcast, broken, scattered and strongly thermally forced cloud fields and are used to perform sensitivity studies to a wider variety of parameters. Comparisons are made at three solar zenith angles (theta (sub 0) = 0, 49, and 63 degrees) to avoid ambiguity in the results due to solar zenith angle.
A theoretical study has been conducted on the effects of cloud horizontal inhomogeneity on cloud albedo bias. A two-dimensional (2D) version of the Spherical Harmonic Discrete Ordinate Method (SHDOM) is used to estimate the albedo bias of the plane parallel (PP-IPA) and independent pixel (IPA-2D) approximations for a wide range of 2D cloud fields obtained from LANDSAT. They include single layer trade cumulus, open and closed cell broken stratocumulus, and solid stratocumulus boundary layer cloud fields over ocean. Findings are presented on a variety of averaging scales and are summarized as a function of cloud fraction, mean cloud optical depth, cloud aspect ratio, standard deviation of optical depth, and the gamma function parameter Y (a measure of the width of the optical depth distribution). Biases are found to be small for small cloud fraction or mean optical depth, where the cloud fields under study behave linearly. They are large (up to 0.20 for PP-IPA bias, -0.12 for IPA-2D bias) for large v. On a scene average basis PP-IPA bias can reach 0.30, while IPA-2D bias reaches its largest magnitude at -0.07. Biases due to horizontal transport (IPA-2D) are much smaller than PP-IPA biases but account for 20% RMS of the bias overall. Limitations of this work include the particular cloud field set used, assumptions of conservative scattering, constant cloud droplet size, no gas absorption or surface reflectance, and restriction to 2D radiative transport. The LANDSAT data used may also be affected by radiative smoothing.
By accounting for surface-based light source emissions and top-of-atmosphere (TOA) downward lunar fluxes, we adapted the spherical harmonics discrete ordinate method (SHDOM) 3-dimensional (3-D) radiative transfer model (RTM) to simulate nighttime 3-D TOA radiances as observed from the Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) on board the Suomi-NPP satellite platform. Used previously for daytime 3-D applications, these new SHDOM enhancements allow for the study of the impacts of various observing conditions and aerosol properties on simulated VIIRS-DNB TOA radiances. Observations over Dakar, Senegal, selected for its bright city lights and a large range of aerosol optical depth (AOD), were investigated for potential applications and opportunities for using observed radiances containing VIIRS-DNB “bright pixels” from artificial light sources to conduct aerosol retrievals. We found that using the standard deviation (SD) of such bright pixels provided a more stable quantity for nighttime AOD retrievals than direct retrievals from TOA radiances. Further, both the mean TOA radiance and SD of TOA radiances over artificial sources are significantly impacted by satellite viewing angles. Light domes, the enhanced radiances adjacent to artificial light sources, are strong functions of aerosol properties and especially aerosol vertical distribution, which may be further utilized for retrieving aerosol layer height in future studies. Through inter-comparison with both day- and nighttime Aerosol Robotic Network (AERONET) data, the feasibility of retrieving nighttime AODs using 3-D RTM SHDOM over artificial light sources was demonstrated. Our study shows strong potential for using artificial light sources for nighttime AOD retrievals, while also highlighting larger uncertainties in quantifying surface light source emissions. This study underscores the need for surface light emission source characterizations as a key boundary condition, which is a complex task that requires enhanced input data and further research. We demonstrate how quality-controlled nighttime light data from NASA’s Black Marble product suite could serve as a primary input into estimations of surface light source emissions for nighttime aerosol retrievals.
Mass concentration (mascon) solutions have become a prominent medium for investigating time-variable gravity recovered by GRACE and GRACE Follow-On. While GRACE Level-2 spherical harmonic products require various post-processing techniques to eliminate correlated noise, mascon formulations employ spatial regularization strategies during the estimation step to improve signal recovery. However, mascon estimation has traditionally required large computing resources and GRACE Level-1B processing capabilities. In this study, we show that a typical mascon estimation system can be reformulated to allow for the estimation of regularized mascons from Level-2 spherical harmonics. Provided that spherical harmonic solution covariances are available, the computed mascons will be mathematically equivalent to similar mascons estimated from Level-1B observations. This method is computationally efficient, better leverages GRACE spherical harmonics than past methods, and matches the performance of typical mascon solutions without locking scientists into pre-determined regularization designs. We develop a proof-of-concept solution using ITSG-Grace2018 and compare results with traditional mascons from JPL and NASA GSFC. We then assess the effects of spherical harmonic truncation and use of regularization correlations on basin signal recovery. We find that spherical expansions to degree and order 60 provide the minimum expansion necessary to study most basins, while larger expansions help further localize signals. We also find that diagonal regularizations (i.e., regularizations that do not contain inter-mascon correlations) are adversely affected by leakage, especially across boundaries such as coastlines where signals are not highly correlated, whereas including inter-mascon correlations and regional boundaries in the regularization greatly improves signal recovery.
A new transport solver option based on the hybrid FEM (HFEM) was implemented in GRIFFIN, the MOOSE-based reactor analysis code, as an effort to support routine core design calculations for advanced reactor applications. The HFEM formulation with P{sub N} (spherical harmonics expansion), akin to the variational nodal method, is effective for solving a spatially homogenized problem with strong transport effect. The residual and Jacobian evaluations of the HFEM weak form were derived and successfully implemented in GRIFFIN, having the diffusion and the PN options available in the new HFEM based transport solver. The performance was tested with the simplified ABTR benchmark problems. The results indicate that the HFEM-based transport solver is a feasible option for solving problems with spatially homogenized and strong streaming by providing superior accuracy with a proper p-refinement. (authors)